Add direct perturbation-based sensitivity coefficient calculation support in STM

[grmnptr]

Closes #28671

[moosebuild]

Job Precheck on 8597158 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/28672/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 6ffbd76688c2c09567f930c89298b6e5a6a403b8

[moosebuild]

Job Documentation on 508b15b wanted to post the following:

View the site here

This comment will be updated on new commits.

[moosebuild]

Job Coverage on 508b15b wanted to post the following:

Framework coverage

Coverage did not change

Modules coverage

Stochastic tools

	6ffbd7	#28672 508b15
	Total	Total	+/-	New
Rate	90.66%	90.68%	+0.02%	91.89%
Hits	7991	8093	+102	102
Misses	823	832	+9	9

Diff coverage report

Full coverage report

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
• thermal_hydraulics
• xfem

This comment will be updated on new commits.

[grmnptr]

Added extra tests like valgrind an everything passes, openmpi failure is not related.