Broadcasting expressions don't work with `deepcopied` ClimaCore spaces

Given that
```julia
using ClimaCore.CommonSpaces
space = CubedSphereSpace(;
radius = 10,
n_quad_points = 4,
h_elem = 10,
)

cop_space = deepcopy(space)

space == cop_space
# false (as expected, that's the point of deepcopying)
```
Fields defined on `space` and cannot be mixed with Fields defined on `cop_space`, even if the two spaces are identical (but not the same)

The issue names no file, test, or entry point. Reproduce the CubedSphereSpace and deepcopy example first, then trace the broadcasting behavior for Fields from the two spaces; done means compatible deepcopied spaces can participate in broadcasting while genuinely incompatible spaces remain distinct.

Written by the indexing model from the issue text.