nightly-2024-06-13: chore: Parse macros (#5229)

# Description

## Problem\*

## Summary\*

To try to make it easier to review I'm breaking the parser related
changes here out #5203.

## Additional Context

It turns out `parser/types.rs` was never in our module tree. I've added
it and removed the duplicate parsers for parsing types that were in
`parser/parser.rs`. They've had some changes since the copies in
`parser/types.rs` were first changed so I've updated those as well.

## Documentation\*

Check one:
- [x] No documentation needed.
- [ ] Documentation included in this PR.
- [ ] **[For Experimental Features]** Documentation to be submitted in a
separate PR.

# PR Checklist\*

- [x] I have tested the changes locally.
- [x] I have formatted the changes with [Prettier](https://prettier.io/)
and/or `cargo fmt` on default settings.