I'm using staging but I can't get it working despite I've inserted manually the row in #_action_logs_extensions. I noticed their is a 2h difference between this PR and committed files in Staging. Are you in sync?

the changes requested

Not sure what is the practice for things intwined between Beta cycle.
This is difficult to test using patch_tester for Upgraded site that are already to 3.9B4 as this PR need other committed stuff already in staging. Can we have the supplemental files in administrator/components/com_admin... ? e.g not only for fresh install

The additions to the #__action_logs_extensions table should be their own SQL files. The changes to the parameter values shouldn't as that changes an existing user configuration (so at most for someone who is already on beta track, they'd just need to go in and re-save the component config adding the new component; keep in mind #21024 has yet to have an "official" response and as such the project does not support upgrades between non-stable releases).

I have tested this item ✅ successfully on 52a5aa2

Test ok on upgraded site.

Note for testers: the below manual actions are required on upgraded site 3.9RC

insert into #__action_logs_extensions values (18, 'com_checkin');
delete from #__extensions where extension_id = 36
insert into #__extensions (extension_id, package_id, name, type, element, folder, client_id, enabled, access, protected, manifest_cache, params, custom_data, system_data, checked_out, checked_out_time, ordering, state) VALUES
(36, 0, 'com_actionlogs', 'component', 'com_actionlogs', '', 1, 1, 1, 1, '', '{"ip_logging":0,"csv_delimiter":",","loggable_extensions":["com_banners","com_cache","com_categories","com_checkin","com_config","com_contact","com_content","com_installer","com_media","com_menus","com_messages","com_modules","com_newsfeeds","com_plugins","com_redirect","com_tags","com_templates","com_users"]}', '', '', 0, '0000-00-00 00:00:00', 0, 0);

What about @mbabker suggestion to have
insert into #__action_logs_extensions values (18, 'com_checkin');
In a separated file ?

After this patch is applied, the tables in the database are not updated.
com_checkin is missing in #__extensions and #__action_logs_extensions tables.

true, this needs some more cares, when it was proposed 3.9 wasn't released yet...
on my todo list

redone with #23526