Swap to an extensible trait-powered design for resolving clashes

[alice-i-cecile]

Hmm. I don't love this design. Doesn't this just get us back to the same place, where UserInput can't be reasonably extended?

Originally posted by @alice-i-cecile in #490 (comment)

[alice-i-cecile]

We want to be able to ensure that we can resolve clashes between inputs, no matter what input kind is there.

The core operation we need is to check if the actions of the two inputs overlap. To do so, we should be using hash sets. We can represent the values in a type-agnostic but reasonably robust way using hashes:

1. Hash the type path of the input.
2. Hash the variant name.
3. Combine these.

Use the power of reflection for good... All of these computations should be able to be mostly cached.

[alice-i-cecile]

This is already completed.