Refactor and DRY up protocol test generation (#3713)

Protocol test generation code was one of the earlier parts of
smithy-rs's codebase and it has accrued a fair amount of tech debt as we
have evolved the code generation primitives. Its code was also forked
when the server code generator was introduced, introducing a lot of
duplicated code that has deviated over time.

This commit refactors the code to modern standards and aims to reconcile
commonalities in `ProtocolTestGenerator`, so that both client and server
can reap centralized improvements over time.

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