Add FE Space quadrature basis choice

[Heinrich-BR]

Closes #30785

Edit: also closes #30652

[moosebuild]

Job Documentation, step Docs: sync website on eb73041 wanted to post the following:

View the site here

This comment will be updated on new commits.

[lindsayad]

Let's try to squash formatting/linting commits

[moosebuild]

Job Coverage, step Generate coverage on eb73041 wanted to post the following:

Framework coverage

	97d074	#30786 eb7304
	Total	Total	+/-	New
Rate	85.53%	85.52%	-0.01%	72.22%
Hits	115364	115415	+51	52
Misses	19517	19536	+19	20

Diff coverage report

Full coverage report

Modules coverage

Coverage did not change

Full coverage reports

Reports

• framework
• chemical_reactions
• combined
• contact
• electromagnetics
• external_petsc_solver
• fluid_properties
• fsi
• functional_expansion_tools
• geochemistry
• heat_transfer
• level_set
• misc
• navier_stokes
• optimization
• peridynamics
• phase_field
• porous_flow
• ray_tracing
• rdg
• reactor
• richards
• scalar_transport
• solid_mechanics
• solid_properties
• stochastic_tools
• subchannel
• thermal_hydraulics
• xfem

Warnings

• framework new line coverage rate 72.22% is less than the suggested 90.0%

This comment will be updated on new commits.

[moosebuild]

Job Precheck, step Clang format on 850faf8 wanted to post the following:

Your code requires style changes.

A patch was auto generated and copied here
You can directly apply the patch by running, in the top level of your repository:

curl -s https://mooseframework.inl.gov/docs/PRs/30786/clang_format/style.patch | git apply -v

Alternatively, with your repository up to date and in the top level of your repository:

git clang-format 97d07485be4caabe405a33494c2a937208d1ff81

[lindsayad]

failure is unrelated