Can this be merged? Similar to SciML/DiffEqBase.jl#1175

No it breaks a lot of tests in its current state and needs to get fixed first

Makes sense. Just noting that this currently stops trimming (or at least JET being happy), but I'm happy to just use this PR branch for now. If others are looking for an alternative dirty fix that also seems to work, I've had success by pirating get_root_indp like so:

import NonlinearSolve.SciMLBase.get_root_indp
NonlinearSolve.SciMLBase.get_root_indp(prob::NonlinearLeastSquaresProblem) = prob.p

It's safe to use. We just have a lot of legacy tests to fix up with this. In particular, we used to have an old method for passing an array of symbols syms and there's a deprecation path etc., all an old undocumented thing that ParameterizedFunctions.jl hooked into, but kept around. It seems that the reason for the complexity here is the deprecation path, so it's fine to just remove it since nothing has used it for probably years now (and it was never user facing or documented), but we need to make sure we do that and update the tests otherwise we'll have breakage. So probably in the next week.

This week we did an entire CI overhaul so we're a bit behind 😅 but we should be moving faster now that everything should be clean.