Just resurfacing this comment by Leo from #344 (comment):

We could probably disable those documentation builds in a separate PR to speed them up?

I’m not too keen on that since he docs builds are a sort of test. But to all builds need to do this (probably only one per OS would be good).

And also at #964 (review):

• Can we set up a matrix build on all 3 OSes in this action? I.e. remove the "Build the documentation" section in ci_tests.yaml and put it here instead.

Rationale: Saves ~4min of CI time. I wanted to separate the tests from the documentation builds in #830, but maybe we can do it in this "Continuous Documentation" workflow instead. I know Leo mentioned using the documentation build as a 'test' before (lazy to dig up that comment), but our >20 min of CI tests is getting wayy too long.

So we should probably run the docs build on only one Python version (e.g. Python 3.9) instead of three (3.7, 3.8, 3.9) to further save on CI resources.

I agree that we should separate "Building the documentation" and "Full tests" into two separate workflows. We can have faster jobs runs and also can control the jobs runs based on files, e.g., we don't want to run the full tests if only gallery examples are changed.

I also agree that we should only build the documentation for one Python version (e.g., 3.9), not three versions.

Closing in favour of alternative implementation at #1033