Skip initialization in eigen problem when restarting

[YaqiWang]

Closes #27621.

[moosebuild]

Job Documentation on d47c4ef wanted to post the following:

View the site here

This comment will be updated on new commits.

[YaqiWang]

Interesting. The failed test here (https://civet.inl.gov/job/2232850/) shows a warning message at the end WARNING! There are options you set that were not used!.

[moosebuild]

Job Coverage on d47c4ef wanted to post the following:

Framework coverage

	dc8a1f	#27622 d47c4e
	Total	Total	+/-	New
Rate	85.09%	85.09%	+0.00%	100.00%
Hits	103153	103155	+2	2
Misses	18077	18075	-2	0

Diff coverage report

Full coverage report

Modules coverage

Coverage did not change

Full coverage reports

Reports

- [`framework`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/framework) - [`chemical_reactions`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/chemical_reactions) - [`combined`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/combined) - [`contact`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/contact) - [`electromagnetics`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/electromagnetics) - [`external_petsc_solver`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/external_petsc_solver) - [`fluid_properties`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/fluid_properties) - [`fsi`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/fsi) - [`functional_expansion_tools`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/functional_expansion_tools) - [`geochemistry`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/geochemistry) - [`heat_transfer`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/heat_transfer) - [`level_set`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/level_set) - [`misc`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/misc) - [`navier_stokes`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/navier_stokes) - [`optimization`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/optimization) - [`peridynamics`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/peridynamics) - [`phase_field`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/phase_field) - [`porous_flow`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/porous_flow) - [`ray_tracing`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/ray_tracing) - [`rdg`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/rdg) - [`reactor`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/reactor) - [`richards`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/richards) - [`scalar_transport`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/scalar_transport) - [`solid_mechanics`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/solid_mechanics) - [`solid_properties`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/solid_properties) - [`stochastic_tools`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/stochastic_tools) - [`thermal_hydraulics`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/thermal_hydraulics) - [`xfem`](https://mooseframework.inl.gov/docs/PRs/27622/coverage/xfem)

This comment will be updated on new commits.

[YaqiWang]

@lindsayad more comments? The failures do not seem relevant.

[lindsayad]

indeed, failures are not related

[YaqiWang]

Thanks @lindsayad!

[loganharbour]

Broke next https://civet.inl.gov/job/2234270/

[loganharbour]

Can someone address this please

[YaqiWang]

That is strange: why p3 and p7 tests pass and p5 does not? Checking.