According to the update log the update was complete and successful. So it seems the error happens after the update when the updater (core or extensions) wants to check for available updates again.

@SniperSister Do you have an idea what goes wrong here?

Can you provide the content of the #__tuf_metadata table?

the table #__tuf_metadata is empty - found this structure:

I think the update pre/post process did not create/update this table as there is no content in it

if you update from beta2 this table couldn't be empty because it's needed by the updater to find a new update.
Did you updated with the online updater or by file upload?

I used the online updater - it indicated a new version and then the update process worked/completed as usual. But then as (a last step?) it ran into this problem.
I guess that the updater corrupted or did a reset of content in #__tuf_metadata table.
I there a way to repair?

you can try to run from https://github.com/joomla/joomla-cms/blob/5.1-dev/administrator/components/com_admin/sql/updates/mysql/5.1.0-2024-02-24.sql

-- The following INSERT statement has been modified to avoid an SQL error
-- when there is more than 1 update site for the Joomla core.
-- See https://github.com/joomla/joomla-cms/pull/43169 for details.
--
INSERT INTO `#__tuf_metadata` (`update_site_id`, `root`)
SELECT ue.`update_site_id`,
       '{"signed":{"_type":"root","spec_version":"1.0","version":2,"expires":"2025-03-02T11:22:17Z","keys":{"07eb082f367c034a95878687f6648aa76d93652b6ee73e58817053d89af6c44f":{"keytype":"ed25519","scheme":"ed25519","keyid_hash_algorithms":["sha256","sha512"],"keyval":{"public":"9b2af2d9b9727227735253d795bd27ea8f0e294a5f3603e822dc5052b44802b9"}},"1b1b1dd55b2c1c7258714cf1c1ae06f23e4607b28c762d016a9d81c48ffe5669":{"keytype":"ed25519","scheme":"ed25519","keyid_hash_algorithms":["sha256","sha512"],"keyval":{"public":"a18e5ebabc19d5d5984b601a292ece61ba3662ab2d071dc520da5bd4f8948799"}},"2dcaf3d0e552f150792f7c636d45429246dcfa34ac35b46a44f5c87cd17d457e":{"keytype":"ed25519","scheme":"ed25519","keyid_hash_algorithms":["sha256","sha512"],"keyval":{"public":"cb0a7a131961a20edea051d6dc2b091fb650bd399bd8514adb67b3c60db9f8f9"}},"31dd7c7290d664c9b88c0dead2697175293ea7df81b7f24153a37370fd3901c3":{"keytype":"ed25519","scheme":"ed25519","keyid_hash_algorithms":["sha256","sha512"],"keyval":{"public":"589d029a68b470deff1ca16dbf3eea6b5b3fcba0ae7bb52c468abc7fb058b2a2"}},"9e41a9d62d94c6a1c8a304f62c5bd72d84a9f286f27e8327cedeacb09e5156cc":{"keytype":"ed25519","scheme":"ed25519","keyid_hash_algorithms":["sha256","sha512"],"keyval":{"public":"6043c8bacc76ac5c9750f45454dd865c6ca1fc57d69e14cc192cfd420f6a66a9"}}},"roles":{"root":{"keyids":["1b1b1dd55b2c1c7258714cf1c1ae06f23e4607b28c762d016a9d81c48ffe5669","2dcaf3d0e552f150792f7c636d45429246dcfa34ac35b46a44f5c87cd17d457e"],"threshold":1},"snapshot":{"keyids":["07eb082f367c034a95878687f6648aa76d93652b6ee73e58817053d89af6c44f","2dcaf3d0e552f150792f7c636d45429246dcfa34ac35b46a44f5c87cd17d457e"],"threshold":1},"targets":{"keyids":["31dd7c7290d664c9b88c0dead2697175293ea7df81b7f24153a37370fd3901c3"],"threshold":1},"timestamp":{"keyids":["9e41a9d62d94c6a1c8a304f62c5bd72d84a9f286f27e8327cedeacb09e5156cc"],"threshold":1}},"consistent_snapshot":true},"signatures":[{"keyid":"2dcaf3d0e552f150792f7c636d45429246dcfa34ac35b46a44f5c87cd17d457e","sig":"2a225a560ec0837b721d4c5e379fedbd3c7c9079a94e6b31e47e0184c8b95421b6036b4286c5d90f29ab4c468d79a712fdb65e96511394ceb3aa8e2b3983a501"},{"keyid":"1b1b1dd55b2c1c7258714cf1c1ae06f23e4607b28c762d016a9d81c48ffe5669","sig":"8ce0b2a7bdc1e6dcba12081f440510df0a593c072dcf591631c2dd0f456844a7da63be8e8ac31ffbddf42641fde84dc733a336031d182c2163b4c1eaf2117005"}]}'
  FROM `#__update_sites_extensions` AS ue JOIN `#__extensions` AS e ON (e.`extension_id` = ue.`extension_id`)
 WHERE e.`type`='file' AND e.`element`='joomla';

UPDATE `#__update_sites`
   SET `type` = 'tuf', `location` = 'https://update.joomla.org/cms/'
 WHERE `update_site_id` IN (SELECT ue.`update_site_id` FROM `#__update_sites_extensions` AS ue JOIN `#__extensions` AS e ON (e.`extension_id` = ue.`extension_id`) WHERE e.`type`='file' AND e.`element`='joomla');

hi,
Thanks a lot - this fixed it! But it is still a puzzle why the update process did wrong (had errors) but did not tell

@jschmi102 It was the update to Beta 1 or Beta 2 where it had failed to fill the table, not the later update to RC 1.

Do you still have the update logs from these previous updates?

logs shows updates starting from 5.02
update.log

@jschmi102 The update to 5.1.0 Beta 1 clearly shows the error:

2024-03-06T08:36:14+00:00	INFO 127.0.0.1	update	Update started by user jochen (62). Old version is 5.1.0-alpha4.
2024-03-06T08:36:16+00:00	INFO 127.0.0.1	update	Downloading update file from https://objects.githubusercontent.com/github-production-release-asset-2e65be/2464908/3291752f-fac1-46d8-82ca-95d04a0cb69a?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAVCODYLSA53PQK4ZA%2F20240306%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240306T083615Z&X-Amz-Expires=300&X-Amz-Signature=d44d8ef1e90f660fb2ddb9dde655931fd09f07271ca320695c2045d28e8fb565&X-Amz-SignedHeaders=host&actor_id=0&key_id=0&repo_id=2464908&response-content-disposition=attachment%3B%20filename%3DJoomla_5.1.0-beta1-Beta-Update_Package.zip&response-content-type=application%2Foctet-stream.
2024-03-06T08:36:20+00:00	INFO 127.0.0.1	update	File 3291752f-fac1-46d8-82ca-95d04a0cb69a downloaded.
2024-03-06T08:36:20+00:00	INFO 127.0.0.1	update	Starting installation of new version.
2024-03-06T08:36:41+00:00	INFO 127.0.0.1	update	Finalising installation.
2024-03-06T08:36:41+00:00	INFO 127.0.0.1	update	Start of SQL updates.
2024-03-06T08:36:41+00:00	INFO 127.0.0.1	update	The current database version (schema) is 5.1.0-2024-02-10.
2024-03-06T08:36:41+00:00	INFO 127.0.0.1	update	Ran query from file 5.1.0-2024-02-24. Query text: CREATE TABLE IF NOT EXISTS `#__tuf_metadata` (   `id` int NOT NULL AUTO_INCREMEN.
2024-03-06T08:36:41+00:00	INFO 127.0.0.1	update	Ran query from file 5.1.0-2024-02-24. Query text: INSERT INTO `#__tuf_metadata` (`update_site_id`, `root`) VALUES ((SELECT ue.`upd.
2024-03-06T08:36:41+00:00	INFO 127.0.0.1	update	JInstaller: :Install: Error SQL Subquery returns more than 1 row
2024-03-06T08:36:41+00:00	INFO 127.0.0.1	update	End of SQL updates - INCOMPLETE.
2024-03-06T08:36:41+00:00	WARNING 127.0.0.1	jerror	JInstaller: :Install: Error SQL Subquery returns more than 1 row

I am pretty sure this error was also shown to the user in the backend.

Maybe you have ignored that error because all was working after that, and then forgotten about it, but it is definitely not true that the error was not shown and not logged anywhere.

The error was fixed in Beta 2 and RC 1 with my PRs #42988 and PR #43169 .

The reason why this error did not cause the described problem before updating to RC1 is because you were on the "Testing" update channel, which uses the old style XML update site. With RC 1 that has been removed, so the TUF based update site is used.

That's why the empty table caused the problem not before the update to RC 1.

Closing as fixed with PRs #42988 and #43169 .