fix: fix several bugs related to remake and symbolic indexing

[AayushSabharwal]

Checklist

• [ ] Appropriate tests were added
• [ ] Any code changes were done in a way that does not break public API
• [ ] All documentation related to code changes were updated
• [ ] The new code follows the contributor guidelines, in particular the SciML Style Guide and COLPRAC.
• [ ] Any new documentation only uses public API

Additional context

Add any other context about the problem here.

[codecov[bot]]

Codecov Report

Attention: 40 lines in your changes are missing coverage. Please review.

Comparison is base (350e3d8) 39.44% compared to head (7ca2602) 0.00%. Report is 81 commits behind head on master.

Files	Patch %	Lines
src/remake.jl	0.00%	26 Missing :warning:
src/solutions/rode_solutions.jl	0.00%	11 Missing :warning:
src/problems/problem_interface.jl	0.00%	3 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #583 +/- ## ========================================== - Coverage 39.44% 0.00% -39.45% ========================================== Files 53 53 Lines 4039 3964 -75 ========================================== - Hits 1593 0 -1593 - Misses 2446 3964 +1518 ```

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[ChrisRackauckas]

Add some inference tests as well.

[ChrisRackauckas]

What's next here?

[AayushSabharwal]

Nothing, it just needs this to be tagged first, which I assume will happen with MTKv9

[ChrisRackauckas]

Looks like there's a circle where tests can't pass?

[AayushSabharwal]

MTK tests should pass regardless of this PR

[ChrisRackauckas]

What's the status of this one?

[AayushSabharwal]

This PR needs https://github.com/SciML/ModelingToolkit.jl/pull/2409 to be tagged

[AayushSabharwal]

TODO: Symbolic remake won't work with SymbolCache as the system as user-provided symbols. I think now that SII exists, process_p_u0_symbolic should be able to be implemented in SciMLBase and be independent of where the symbols come from?

[AayushSabharwal]

CI won't pass here until https://github.com/SciML/ModelingToolkit.jl/pull/2409 is merged and tagged. I also have plans to remove process_p_u0_symbolic from MTK and just handle it in SciMLBase using SII. This would allow for symbolic initialization using DSLs (SymbolCache) as well.

[isaacsas]

Is there any update on this or the PRs this requires before it can be merged?

[AayushSabharwal]

This PR is too old to be merged, and the required changes are now different than what this PR intended. I'll open a new one soon