Fixes https://github.com/JuliaLang/julia/issues/56134
After this,
```julia
julia> using LinearAlgebra

julia> A = hermitianpart(rand(4, 4))
4×4 Hermitian{Float64, Matrix{Float64}}:
 0.387617  0.277226  0.67629   0.60678
 0.277226  0.894101  0.388416  0.489141
 0.67629   0.388416  0.100907  0.619955
 0.60678   0.489141  0.619955  0.452605

julia> B = UpperTriangular(A)
4×4 UpperTriangular{Float64, Hermitian{Float64, Matrix{Float64}}}:
 0.387617  0.277226  0.67629   0.60678
  ⋅        0.894101  0.388416  0.489141
  ⋅         ⋅        0.100907  0.619955
  ⋅         ⋅         ⋅        0.452605

julia> B - B'
4×4 Matrix{Float64}:
  0.0        0.277226   0.67629   0.60678
 -0.277226   0.0        0.388416  0.489141
 -0.67629   -0.388416   0.0       0.619955
 -0.60678   -0.489141  -0.619955  0.0
```
This preserves the band structure of the parent, if any:
```julia
julia> U = UpperTriangular(Diagonal(ones(4)))
4×4 UpperTriangular{Float64, Diagonal{Float64, Vector{Float64}}}:
 1.0  0.0  0.0  0.0
  ⋅   1.0  0.0  0.0
  ⋅    ⋅   1.0  0.0
  ⋅    ⋅    ⋅   1.0

julia> U - U'
4×4 Diagonal{Float64, Vector{Float64}}:
 0.0   ⋅    ⋅    ⋅ 
  ⋅   0.0   ⋅    ⋅ 
  ⋅    ⋅   0.0   ⋅ 
  ⋅    ⋅    ⋅   0.0
```
This doesn't fully work with partly initialized matrices, and would need
#55312 for that.

The abstract triangular methods now construct matrices using
`similar(parent(U), size(U))` so that the destinations are fully
mutable.
```julia
julia> @invoke B::LinearAlgebra.AbstractTriangular - B'::LinearAlgebra.AbstractTriangular
4×4 Matrix{Float64}:
  0.0        0.277226   0.67629   0.60678
 -0.277226   0.0        0.388416  0.489141
 -0.67629   -0.388416   0.0       0.619955
 -0.60678   -0.489141  -0.619955  0.0
```

---------

Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>

Backported PRs:
- [x] #55886 <!-- irrationals: restrict assume effects annotations to
known types -->
- [x] #55867 <!-- update `hash` doc string: `widen` not required any
more -->
- [x] #56084 <!-- slightly improve inference in precompilation code -->
- [x] #56088 <!-- make `Base.ANSIIterator` have a concrete field -->
- [x] #54093 <!-- Fix `JULIA_CPU_TARGET` being propagated to workers
precompiling stdlib pkgimages -->
- [x] #56165 <!-- Fix markdown list in installation.md -->
- [x] #56148 <!-- Make loading work when stdlib deps are missing in the
manifest -->
- [x] #56174 <!-- Fix implicit `convert(String, ...)` in several places
-->
- [x] #56159 <!-- Add invalidation barriers for `displaysize` and
`implicit_typeinfo` -->
- [x] #56089 <!-- Call `MulAddMul` instead of multiplication in
_generic_matmatmul! -->
- [x] #56195 <!-- Include default user depot when JULIA_DEPOT_PATH has
leading empty entry -->
- [x] #56215 <!-- [REPL] fix lock ordering mistake in load_pkg -->
- [x] #56251 <!-- REPL: run repl hint generation for modeswitch chars
when not switching -->
- [x] #56092 <!-- stream: fix reading LibuvStream into array -->
- [x] #55870 <!-- fix infinite recursion in `promote_type` for
`Irrational` -->
- [x] #56227 <!-- Do not call `rand` during sysimage precompilation -->
- [x] #55741 <!-- Change annotations to use a NamedTuple -->
- [x] #56149 <!-- Specialize adding/subtracting mixed
Upper/LowerTriangular -->
- [x] #56214 <!-- fix precompile process flags -->
- [x] #54471
- [x] #55622
- [x] #55704
- [x] #55764