Finish making legacycustomsearches optional

Our long term goal is to stop supporting the legacycustomsearch framework (and eventually the rest of the legacy search framework). We have a way to go before this is possible. However, we are already providing de facto limited support for the extension in that we are really only doing the following:

1. doing work that involves getting the extension code out of core & into the core extension
2. doing php8.2 updates (begrudingly)
3. merging bug fixes
4. addressing regressions

This mostly means that features, in particular, are no longer being added.

We are now in a good position to work towards the interim goal of shipping CiviCRM with the extension disabled.

In order to do this I have found a few places where the extension needs to come out of the core code

1. The fillPrevNextCache functionality - this doesn't need to be shared with the core search - and by unsharing we can simplify all that isCoreSearch stuff. I put up a PR after doing universe grepping https://github.com/civicrm/civicrm-core/pull/25392

2. The export task functionality - a separate path for the custom searches is embedded in the core searches. I got this within a whisper of working in the past & will try to revive that work https://github.com/civicrm/civicrm-core/pull/25504

3. CRM_Contact_BAO_SearchCustom needs to be moved to the extension

4. The shared but nah-not-really code in contactIDSQL needs to come out of the core code

5. This is probably the one that needs most thought - the code to build the group contact cache needs to not be called directly from that class - ie we need a listener of some sort available - currently the code is 'if api4 then x, if custom search then y, if legacy core search then z' - so all 3 would probably 'listen & do' https://github.com/civicrm/civicrm-core/pull/26611

7. Query formatter appears to be entirely part of the FullTextSearch CRM_Utils_QueryFormatter

8. Many but not all of these places are covered above - but they all need to be out of CRM