sagemathgh-36498: CI build, doc-build: Run containers explicitly, separate jobs for pyright, build, modularized tests, long tests
    
<!-- ^^^^^
Please provide a concise, informative and self-explanatory title.
Don't put issue numbers in there, do this in the PR body below.
For example, instead of "Fixes sagemath#1234" use "Introduce new method to
calculate 1+1"
-->
<!-- Describe your changes here in detail -->

<!-- Why is this change required? What problem does it solve? -->
Running the containers explicitly, instead of using the declarative
`container:` feature of GH Actions gives us more control:
- we can create more space on the host if necessary; we just scraped by
an out of space condition in sagemath#36473 /
sagemath#36469 (comment)
- we can run some operations outside of the container but in the same
job; this will make the separate "Get CI fixes" jobs unnecessary,
addressing the cosmetic concerns from
sagemath#36338 (comment),
sagemath#36349
- it enables caching between the various workflows (as first discussed
in sagemath#36446).

We split out static type checking with pyright into its separate
workflow:
- **pyright.yml**: As static checking does not need  a build of the Sage
library, for PRs that do not make any changes to packages, there's
nothing to build, and the workflow gives a fast turnaround just after 10
minutes. For applying the CI fixes from blocker tickets, this workflow
uses the technique favored in sagemath#36349.

The workflow **build.yml** first launches a job:
- **test-new:** It builds incrementally (using a tox-generated
`Dockerfile` and https://github.com/marketplace/actions/build-and-push-
docker-images) and does the quick incremental test. This completes
within 10 to 20 minutes when there's no change.

After this is completed, more jobs are launched:
- **test-mod:** It again builds incrementally and tests a modularized
distribution. Later (with more from sagemath#35095), more jobs will be added to
this matrix job for other distributions.
- **test-long:** It again builds incrementally and runs the long test.

The workflows **doc-build.yml** and **doc-build-pdf.yml** again build
incrementally and then build the documentation. The diffing code for the
HTML documentation now runs in the host, not the container, which
simplifies things. (To show that diffing still works, we include a small
change to the Sage library.)

Splitting the workflow jobs implements @kwankyu's  suggestion from:
- sagemath#35652 (comment)
(Fixes sagemath#35814)

The steps "again builds incrementally" actually use the GH Actions
cache, https://docs.docker.com/build/ci/github-actions/cache/#cache-
backend-api. When nothing is cached and the 3 workflows are launched in
parallel, they may each build the same thing. But when there's
congestion that leads to the workflows to be run serially, the 2nd and
3rd workflow will be able to use the cache from the 1st workflow. This
elasticity may be helpful in reducing congestion.

There is a rather small per-project limit of 10 GB for this cache, so
we'll have to see how effectively caching works in practice. See
https://github.com/sagemath/sage/actions/caches


<!-- If this PR resolves an open issue, please link to it here. For
example "Fixes sagemath#12345". -->
<!-- If your change requires a documentation PR, please link it
appropriately. -->

### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->
<!-- If your change requires a documentation PR, please link it
appropriately -->
<!-- If you're unsure about any of these, don't hesitate to ask. We're
here to help! -->
<!-- Feel free to remove irrelevant items. -->

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on
- sagemath#12345: short description why this is a dependency
- sagemath#34567: ...
-->
- Depends on sagemath#36938 (merged here)
- Depends on sagemath#36951 (merged here)
- Depends on sagemath#37351 (merged here)
- Depends on sagemath#37750 (merged here)

<!-- If you're unsure about any of these, don't hesitate to ask. We're
here to help! -->
    
URL: sagemath#36498
Reported by: Matthias Köppe
Reviewer(s): Kwankyu Lee, Matthias Köppe

sagemathgh-36498: CI build, doc-build: Run containers explicitly, separate jobs for pyright, build, modularized tests, long tests
    
<!-- ^^^^^
Please provide a concise, informative and self-explanatory title.
Don't put issue numbers in there, do this in the PR body below.
For example, instead of "Fixes sagemath#1234" use "Introduce new method to
calculate 1+1"
-->
<!-- Describe your changes here in detail -->

<!-- Why is this change required? What problem does it solve? -->
Running the containers explicitly, instead of using the declarative
`container:` feature of GH Actions gives us more control:
- we can create more space on the host if necessary; we just scraped by
an out of space condition in sagemath#36473 /
sagemath#36469 (comment)
- we can run some operations outside of the container but in the same
job; this will make the separate "Get CI fixes" jobs unnecessary,
addressing the cosmetic concerns from
sagemath#36338 (comment),
sagemath#36349
- it enables caching between the various workflows (as first discussed
in sagemath#36446).

We split out static type checking with pyright into its separate
workflow:
- **pyright.yml**: As static checking does not need  a build of the Sage
library, for PRs that do not make any changes to packages, there's
nothing to build, and the workflow gives a fast turnaround just after 10
minutes. For applying the CI fixes from blocker tickets, this workflow
uses the technique favored in sagemath#36349.

The workflow **build.yml** first launches a job:
- **test-new:** It builds incrementally (using a tox-generated
`Dockerfile` and https://github.com/marketplace/actions/build-and-push-
docker-images) and does the quick incremental test. This completes
within 10 to 20 minutes when there's no change.

After this is completed, more jobs are launched:
- **test-mod:** It again builds incrementally and tests a modularized
distribution. Later (with more from sagemath#35095), more jobs will be added to
this matrix job for other distributions.
- **test-long:** It again builds incrementally and runs the long test.

The workflows **doc-build.yml** and **doc-build-pdf.yml** again build
incrementally and then build the documentation. The diffing code for the
HTML documentation now runs in the host, not the container, which
simplifies things. (To show that diffing still works, we include a small
change to the Sage library.)

Splitting the workflow jobs implements @kwankyu's  suggestion from:
- sagemath#35652 (comment)
(Fixes sagemath#35814)

The steps "again builds incrementally" actually use the GH Actions
cache, https://docs.docker.com/build/ci/github-actions/cache/#cache-
backend-api. When nothing is cached and the 3 workflows are launched in
parallel, they may each build the same thing. But when there's
congestion that leads to the workflows to be run serially, the 2nd and
3rd workflow will be able to use the cache from the 1st workflow. This
elasticity may be helpful in reducing congestion.

There is a rather small per-project limit of 10 GB for this cache, so
we'll have to see how effectively caching works in practice. See
https://github.com/sagemath/sage/actions/caches


<!-- If this PR resolves an open issue, please link to it here. For
example "Fixes sagemath#12345". -->
<!-- If your change requires a documentation PR, please link it
appropriately. -->

### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->
<!-- If your change requires a documentation PR, please link it
appropriately -->
<!-- If you're unsure about any of these, don't hesitate to ask. We're
here to help! -->
<!-- Feel free to remove irrelevant items. -->

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on
- sagemath#12345: short description why this is a dependency
- sagemath#34567: ...
-->
- Depends on sagemath#36938 (merged here)
- Depends on sagemath#36951 (merged here)
- Depends on sagemath#37351 (merged here)
- Depends on sagemath#37750 (merged here)

<!-- If you're unsure about any of these, don't hesitate to ask. We're
here to help! -->
    
URL: sagemath#36498
Reported by: Matthias Köppe
Reviewer(s): Kwankyu Lee, Matthias Köppe