Update BCS for forward recomputation

[Ig-dolci]

Description

This PR seeks to fix the issue #4387, which is related to the Nonlinear Variational Solve not updating the Dirichlet boundary conditions based on the checkpointed functions.

[Ig-dolci]

It is still missing a test for this case.

[pbrubeck]

You will get this case by passing pre_apply_bcs=False to the NLVS

[Ig-dolci]

Thank you.

[pbrubeck]

Can this logic be put into a new property that gets overloaded in the corresponding adjoint subclass of DirichletBC?

[Ig-dolci]

Yes, it must be. I am still checking to see if this works. It looks like it requires more thought. Sia just wrote that this is leading some Gadopt tests to fail.

[sghelichkhani]

I know this is still wip, but flagging that this breaks one of our tests and the unit test here. Our CI is failing as we load the BC from a checkpoint file:

  File "/opt/firedrake/firedrake/bcs.py", line 461, in apply
    r.assign(bc, subset=self.node_set)
  File "/opt/firedrake/firedrake/adjoint_utils/function.py", line 116, in wrapper
    ret = assign(self, other, *args, **kwargs)
          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/opt/firedrake/firedrake/function.py", line 461, in assign
    Assigner(self, expr, subset).assign()
    ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/opt/firedrake/firedrake/assign.py", line 147, in __init__
   expression = as_ufl(expression)
                 ^^^^^^^^^^^^^^^^^^
  File "/usr/local/lib/python3.12/dist-packages/ufl/constantvalue.py", line 517, in as_ufl
    raise ValueError(
ValueError: Invalid type conversion: <firedrake.adjoint_utils.checkpointing.DelegatedFunctionCheckpoint object at 0x
73029d9272f0> can not be converted to any UFL type.