Add cache to `get_tags_for_room(...)`

This helps Sliding Sync because `get_tags_for_room(...)` is going to be
used in https://github.com/element-hq/synapse/pull/17695

Essentially, we're just trying to match `get_account_data_for_room(...)`
which already has a tree cache.

No need to sort if the range is large enough to cover all of the rooms
in the list. Previously, we would only do this optimization if the range
was exactly large enough.

Follow-up to https://github.com/element-hq/synapse/pull/17672

Fix `_bulk_get_max_event_pos(...)` being inefficient. It kept adding all
of the `batch_results` to the `results` over and over every time we
checked a single room in the batch.

I think we still ended up with the right answer before because we
accumulate `recheck_rooms` and actually recheck them to overwrite the
bad data we wrote to the `results` before.

Introduced in
https://github.com/element-hq/synapse/pull/17606/files#diff-cbd54e4b5a2a1646299d659a2d5884d6cb14e608efd2e1658e72b465bb66e31bR1481

`m.ignored_user_list` in account data

Shortcut for checking if certain background updates have completed

Pulling this change out from one of @erikjohnston's branches
(https://github.com/element-hq/synapse/compare/develop...erikj/ss_perf

)

---------

Co-authored-by: Erik Johnston <erikj@element.io>

Fixes https://github.com/element-hq/element-x-ios/issues/3300

Some rooms are missing from `sliding_sync_joined_rooms`. When this
happens, the first call will succeed, but any subsequent calls for this
room ID will cause the cache to return `None` for the room ID, rather
than not having the key at all. This then causes the `<=` check to
throw.

Root cause: https://github.com/element-hq/synapse/issues/17726

### Pull Request Checklist

<!-- Please read
https://element-hq.github.io/synapse/latest/development/contributing_guide.html
before submitting your pull request -->

* [x] Pull request is based on the develop branch
* [ ] Pull request includes a [changelog
file](https://element-hq.github.io/synapse/latest/development/contributing_guide.html#changelog).
The entry should:
- Be a short description of your change which makes sense to users.
"Fixed a bug that prevented receiving messages from other servers."
instead of "Moved X method from `EventStore` to `EventWorkerStore`.".
  - Use markdown where necessary, mostly for `code blocks`.
  - End with either a period (.) or an exclamation mark (!).
  - Start with a capital letter.
- Feel free to credit yourself, by adding a sentence "Contributed by
@github_username." or "Contributed by [Your Name]." to the end of the
entry.
* [ ] [Code
style](https://element-hq.github.io/synapse/latest/code_style.html) is
correct
(run the
[linters](https://element-hq.github.io/synapse/latest/development/contributing_guide.html#run-the-linters))

We only need to check it if returned bump stamp is `None`, which is rare.

Pulling this change out from one of @erikjohnston's branches
(https://github.com/element-hq/synapse/compare/develop...erikj/ss_perf)

The account data extension was also updated to avoid copies when we pull
the data out of the cache.

Fix https://github.com/element-hq/synapse/issues/17694

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This appears to be enough to make Element Web work (or at least move it
on to the next hurdle)

---------

Co-authored-by: Eric Eastwood <eric.eastwood@beta.gouv.fr>

For initial requests a typical page size is 20 rooms, so we may as well
do the batching as 20.

This should speed up bigger syncs a little bit.

Move filters tests to rest layer in order to test the new (with sliding
sync tables) and fallback paths that Sliding Sync can use.

Also found a bug in the new path because it's not being tested which is
also fixed in this PR. We now take into account `has_known_state` when
filtering.

Spawning from
https://github.com/element-hq/synapse/pull/17662#discussion_r1755574791.
This should have been done when we started using the new sliding sync
tables in https://github.com/element-hq/synapse/pull/17630

This PR changes `from pydantic import BaseModel` to `from
synapse._pydantic_compat import BaseModel` (as well as `constr`,
`conbytes`, `conint`, `confloat`).

It allows `check_pydantic_models.py` to mock those pydantic objects only
in the synapse module, and not interfere with pydantic objects in
external dependencies.

This should solve the CI problems for #17144, which breaks because
`check_pydantic_models.py` patches pydantic models from
[scim2-models](https://scim2-models.readthedocs.io/).

/cc @DMRobertson @gotmax23
fixes #17659 


### Pull Request Checklist

<!-- Please read
https://element-hq.github.io/synapse/latest/development/contributing_guide.html
before submitting your pull request -->

* [x] Pull request is based on the develop branch
* [x] Pull request includes a [changelog
file](https://element-hq.github.io/synapse/latest/development/contributing_guide.html#changelog).
The entry should:
- Be a short description of your change which makes sense to users.
"Fixed a bug that prevented receiving messages from other servers."
instead of "Moved X method from `EventStore` to `EventWorkerStore`.".
  - Use markdown where necessary, mostly for `code blocks`.
  - End with either a period (.) or an exclamation mark (!).
  - Start with a capital letter.
- Feel free to credit yourself, by adding a sentence "Contributed by
@github_username." or "Contributed by [Your Name]." to the end of the
entry.
* [x] [Code
style](https://element-hq.github.io/synapse/latest/code_style.html) is
correct
(run the
[linters](https://element-hq.github.io/synapse/latest/development/contributing_guide.html#run-the-linters))

Use Sliding Sync tables for sorting
(`bulk_get_last_event_pos_in_room_before_stream_ordering(...)` ->
`_bulk_get_max_event_pos(...)`)

Sliding Sync: Make sure we get up-to-date information from `get_sliding_sync_rooms_for_user(...)` (#17692)

We need to bust the `get_sliding_sync_rooms_for_user`
cache when the room encryption is updated and any
other field that is used in the query.

Follow-up to https://github.com/element-hq/synapse/pull/17630

- Bust cache for membership change (cross-reference
`get_rooms_for_user`)
- Bust cache for room `encryption` (cross-reference
`get_room_encryption`)
- Bust cache for `forgotten` (cross-reference
`did_forget`/`get_forgotten_rooms_for_user`)

For rooms with a name we can skip fetching a full room summary, as we
don't need to calculate heroes, and instead just fetch the room counts
directly.

This also changes things to not return counts and heroes for non-joined
rooms. For left/banned rooms we were returning zero values anyway, and
for invite/knock rooms we don't really want to leak such information
(even if some of is included in the stripped state).

For rooms with a name we can skip fetching a full room summary, as we
don't need to calculate heroes, and instead just fetch the room counts
directly.

This also changes things to not return counts and heroes for non-joined
rooms. For left/banned rooms we were returning zero values anyway, and
for invite/knock rooms we don't really want to leak such information
(even if some of is included in the stripped state).

Co-authored-by: Andrew Morgan <1342360+anoadragon453@users.noreply.github.com>

Co-authored-by: dependabot[bot] <49699333+dependabot[bot]@users.noreply.github.com>

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