This fixes #8319.

This takes about 10 seconds in the best case; often more.

Fix unread counts making sync fail if the value of the `unread_count`
column in `event_push_summary` is `None`.

I'm hoping this will provide some pointers for debugging
https://github.com/matrix-org/synapse/issues/7968.

All the callers want this info in the same place, so let's reduce the
duplication by doing it here.

* Fixup `ALTER TABLE` database queries

Make the new columns nullable, because doing otherwise can wedge a
server with a big database, as setting a default value rewrites the
table.

* Switch back to using the notifications count in the push badge

Clients are likely to be confused if we send a push but the badge count
is the unread messages one, and not the notifications one.

* Changelog

Regressed in #8037.

Co-authored-by: Patrick Cloke <clokep@users.noreply.github.com>

* Revert "Add experimental support for sharding event persister. (#8170)"

This reverts commit 82c1ee1c.

* Changelog

Co-authored-by: Richard van der Hoff <1389908+richvdh@users.noreply.github.com>

I think this is simpler (and moves stuff out of the db threads)

This requires adding a mypy plugin to fiddle with the type signatures a bit.

We have three things which all call `_get_e2e_device_keys_and_signatures_txn`
with their own `runInteraction`. Factor out the common code.