Introduce support for MSC4429: Profile Updates for Legacy Sync (#19556)

Implements support for [MSC4429: Profile Updates for Legacy
Sync](https://github.com/matrix-org/matrix-spec-proposals/pull/4429).

Paired with https://github.com/matrix-org/complement/pull/849 and
https://github.com/matrix-org/sytest/tree/anoa/msc4429

Tracking issue for removing unstable identifiers in Synapse:
https://github.com/element-hq/synapse/issues/19891
Further improvements tracked in:
https://github.com/element-hq/synapse/issues/19981

---------

Co-authored-by: Half-Shot <will@half-shot.uk>
Co-authored-by: Jason Robinson <jasonr@element.io>
Co-authored-by: Olivier 'reivilibre' <oliverw@element.io>

scripts-dev/mypy_synapse_plugin.py

@@ -45,6 +45,7 @@ from mypy.types import (
     AnyType,
     CallableType,
     Instance,
+    LiteralType,
     NoneType,
     Options,
     TupleType,
@@ -813,6 +814,10 @@ def is_cacheable(
     if isinstance(rt, AnyType):
         return True, ("may be mutable" if verbose else None)
 
+    elif isinstance(rt, LiteralType):
+        # Literal[True] etc
+        return True, None
+
     elif isinstance(rt, Instance):
         if (
             rt.type.fullname in IMMUTABLE_VALUE_TYPES