The main motivation of this PR is to fix #55807.
dc689fe tries to remove the slow
`may_contain_union_decision` check by re-organizing the code path. Now
the fast path has been removed and most of its optimization has been
integrated into the preserved slow path.
Since the slow path stores all inner ∃ decisions on the outer most R
stack, there might be overflow risk.
aee69a4 should fix that concern.

The reported MWE now becomes
```julia
  0.000002 seconds
  0.000040 seconds (105 allocations: 4.828 KiB, 52.00% compilation time)
  0.000023 seconds (105 allocations: 4.828 KiB, 49.36% compilation time)
  0.000026 seconds (105 allocations: 4.828 KiB, 50.38% compilation time)
  0.000027 seconds (105 allocations: 4.828 KiB, 54.95% compilation time)
  0.000019 seconds (106 allocations: 4.922 KiB, 49.73% compilation time)
  0.000024 seconds (105 allocations: 4.828 KiB, 52.24% compilation time)
```

Local bench also shows that 72855cd slightly accelerates
`OmniPackage.jl`'s loading
```julia
julia> @time using OmniPackage
# v1.11rc4
 20.525278 seconds (25.36 M allocations: 1.606 GiB, 8.48% gc time, 12.89% compilation time: 77% of which was recompilation)
# v1.11rc4+aee69a4+72855cd
 19.527871 seconds (24.92 M allocations: 1.593 GiB, 8.88% gc time, 15.13% compilation time: 82% of which was recompilation)
```

(cherry picked from commit f3a36d7)

This PR is a potential fix for #54833.

## Description
The function
https://github.com/JuliaLang/julia/blob/2a06376c18afd7ec875335070743dcebcd85dee7/stdlib/LinearAlgebra/src/triangular.jl#L2220
computes $\boldsymbol{A}^{\dfrac{1}{2^s}} - \boldsymbol{I}$ for a
real-valued $2\times 2$ matrix $\boldsymbol{A}$ using Algorithm 5.1 in
[R1]. However, the algorithm in [R1] as well as the above function do
not handle the case $s=0.$ This fix extends the function to compute
$\boldsymbol{A}^{\dfrac{1}{2^s}} - \boldsymbol{I} \Bigg|_{s=0} =
\boldsymbol{A} - \boldsymbol{I}.$

## Checklist
- [X] Fix code: `stdlib\LinearAlgebra\src\triangular.jl` in function
`_sqrt_pow_diag_block_2x2!(A, A0, s)`.
- [X] Add test case: `stdlib\LinearAlgebra\test\triangular.jl`.
- [X] Update `NEWS.md`.
- [X] Testing and self review.

|  Tag  | Reference |
| --- | --- |
| <nobr>[R1]</nobr> | Al-Mohy, Awad H. and Higham, Nicholas J. "Improved
Inverse Scaling and Squaring Algorithms for the Matrix Logarithm", 2011,
url: https://eprints.maths.manchester.ac.uk/1687/1/paper11.pdf |

---------

Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>
Co-authored-by: Oscar Smith <oscardssmith@gmail.com>
(cherry picked from commit 2cdfe06)

…#57138)

(cherry picked from commit 88c71dd)

Ref: #57250.

Fixes
#54560 (comment)

(cherry picked from commit 79e98e3)

Comparing objects by `==` will happily answer nonsense for malformed
type comparisons, such as `unwrap_unionall(A) == A`. Avoid forming that
query. Additionally, need to recourse through Vararg when examining type
structure to make decisions.

Fix #55076
Fix #55189

(cherry picked from commit 32ea18e)

This fixes up a couple of conspicuous problems I noticed when reviewing

I'm unsure we should have accepted this pass in Base to begin with... It
should at least be re-written to error on unexpected IR elements
(instead of performing an invalid transform silently), but the real
problem is that this pass is out-of-pipeline and so it doesn't run on
most user code and we have much worse coverage compared to passes in the
main Compiler.

(cherry picked from commit c1db3a4)

…lignment to LLVM (#56938)

Fixes #56937

---------

Co-authored-by: Oscar Smith <oscardssmith@gmail.com>
(cherry picked from commit 1e2758e)

…ead of the attempted written bytes. (#56980)

(cherry picked from commit 6ac351a)

PR #51317 was a bit over-eager about inferring inferring unreachable
code methods. Filter out the Vararg case, since that can be handled by
simply removing it instead of discarding the whole call.

Fixes #56628

(cherry picked from commit eb9f24c)

…e heap alignment to LLVM (#56938)"

This reverts commit 09704c7.