Adopt `ParamSpec` for type hints

This issue has been migrated from [#11711](https://github.com/matrix-org/synapse/issues/11711).

---

[PEP-612](https://www.python.org/dev/peps/pep-0612/) adds `ParamSpec`, which will allow us to correctly annotate:
* Decorators which preserve parameters and return types. These will no longer require `cast`s.
* Decorators which change the return type can be correctly annotated and type checked.
* Basically anything that handles `*args` and `**kwargs`.

**mypy 0.931**
(blocked on #11712)

As of mypy 0.931, basic `ParamSpec` usage is supported, plus `P.args` and `P.kwargs`. These styles of function can be annotated:
```py
def decorate(f: Callable[P, R]) -> Callable[P, Optional[R]]:
def wrapped(*args: P.args, **kwargs: P.kwargs) -> Optional[R]:
...
```
```py
def call(f: Callable[P, R], *args: P.args, **kwargs: P.kwargs) -> R:
...
```
`Concatenate` and `def call(f: Callable[P, R], *args: P.args, some_flag: bool = False, **kwargs: P.kwargs)` (extra kwarg) don't work yet.

Start by reading PEP 612 and checking the stated mypy 0.931 support for ParamSpec, P.args, and P.kwargs. Search the Synapse codebase for decorators and functions handling *args and **kwargs, then assess whether their annotations can adopt ParamSpec without casts; account for the stated Concatenate limitations.

Written by the indexing model from the issue text.