Interface/type class system redesign

At the moment Dex features a fairly primitive interface system, at least when compared to e.g. Haskell. This is the main issue to track progress on its redesign.
- [x] https://github.com/google-research/dex-lang/issues/666
- [x] https://github.com/google-research/dex-lang/issues/667
- [x] https://github.com/google-research/dex-lang/issues/668
- [ ] https://github.com/google-research/dex-lang/issues/669
- [ ] https://github.com/google-research/dex-lang/issues/621
- [ ] https://github.com/google-research/dex-lang/issues/460
- [ ] https://github.com/google-research/dex-lang/issues/670
- [x] https://github.com/google-research/dex-lang/issues/680
- [x] #1150
- [x] https://github.com/google-research/dex-lang/issues/186

Additionally and optionally:
- [ ] https://github.com/google-research/dex-lang/issues/671
- [ ] https://github.com/google-research/dex-lang/issues/340
- [ ] Explicit application with named instances (while preserving coherence as in e.g. [this paper](https://dl.acm.org/doi/10.1145/3299711.3242752))
- [ ] Have a more compact syntax for defining a long superclass chain (e.g. define `Field` and derive `Eq`, `Add`, `Mul`, etc.)
- [ ] Support polymorphism over records (Eq for records).

Start by reviewing the linked issues 666, 667, 668, 669, 621, 460, 670, 680, 1150, 186, 671, and 340 to understand which redesign work remains. The optional items also mention named instances, superclass-chain syntax, and polymorphism over records. Done means completing a clearly scoped remaining checklist item rather than the full redesign.

Written by the indexing model from the issue text.