In `send_push_notifications`, we were manually asserting types of the
fields returned by the `remotes/push/e2ee/notify` endpoint at runtime
and constructed the `response_data` data structure for further use.
Pydantic is the perfect tool for this task.
This commit updates the concerned code to use Pydantic's `TypeAdapter`.
No functional change.
Fixes part of #35368.
(cherry picked from commit 5a37942c61)