The pre upgrade checker does not block anything it is 'just' an info tool for you to plan the mirgation right now.

Concerning com_search: see https://docs.joomla.org/Joomla_3.x_to_4.x_Step_by_Step_Migration#Notes_on_Search_.28com_search.29

Notes on Search (com_search)

Search (com_search) will be decoupled in Joomla 4.x. Search (com_search) will migrate to Joomla 4. After migration, you'll need to update it to the Joomla 4.x version via com_installer. It will continue to be maintained, but more the same way a third-party extension is by receiving updates via com_installer. It is recommended to use Smart Search (com_finder) going forward. Search will still be available at https://extensions.joomla.org/category/official-extensions/ .

I'm not sure if it's this repository: https://github.com/joomla-extensions/search

All I know is that com_search doesn't break the backend on updates from Joomla 3 to 4. Haven't tested more yet.

I'm not sure if it's this repository: https://github.com/joomla-extensions/search

Yes it is that repo :)

com_search is not removed from existing sites. We don't want to break them. com_search will have a 4.0-compatible version, which we are going to maintain until Joomla 5.0. It is correct that com_search is not removed on update.

There is no secret, most people take the system "as is", without further thought. I would suggest a step to summarize about extensions not natively found in Joomla! 4. (Separated into "deprecated" and "self-installed")

The minimum number of cases update will be done by the person who installed the earlier version. Such a list would help me determine if I still want to use them.

A list is now provided with detailed information in the pre-update check. It was not available at the time of this report

I am unable to verify this now. I can publicize the base, but the "moment" will it take before the necessary files is uncovered.

Closing. If there are specific migration issues, please open new issues. Thanks.