Probably this issue #40412?

Thank you for reporting this error.
It probably related to the issue we have documented here https://docs.joomla.org/J4.x:Error_setCookie().
Please test that the workaround fixes your issue (change the cookie lifetime from 'Year' to 'Session' in the System plugin 'Language filter').

It is a different issue. This sounds the same as the one that I had at #40226

Open the file: \Joomla\administrator\cache\autoload_psr4.php

Do you miss the following line?
'Joomla\\Plugin\\Authentication\\Cookie\\' => [JPATH_PLUGINS . '\authentication/cookie/src'],

Then remember me was checked. The error message is then caused by the missing line.

@sandewt Thanks! But it doesn't work for me and I haven't missed this line either.
'Joomla\\Plugin\\Authentication\\Cookie\\' => [JPATH_PLUGINS . '/authentication/cookie/src'],

Deleting the file \Joomla\administrator\cache\autoload_psr4.php did not change anything either.

Reinstalling the Joomla 4.3.0 files did not bring anything either.

Fortunately there are backups :)

At the backend login, it displayed the following message at the end.
Failed opening required '/plugins/authentication/joomla/joomla.php

At the backend login, it displayed the following message at the end.

No idea.

Advice: don't show the whole path to the joomla.php file on the internet, /plugins/authentication/joomla/joomla.php is enough information about the location. You can edit your comment.

We're having a very similar issue when upgrading to 4.3.0 on a relatively fresh install (late last year) of Joomla 4 on Ubuntu:

Class "Joomla\Plugin\System\GuidedTours\Extension\GuidedTours" not found

After disabling that plugin, the error changed to the "Content\Contact" plugin, then after disabling that one to the "EmailCloak" plugin.

Deleting/recreating the autoload_psr4.php file did not help, nor did a manual load of the 4.3.0 update tar.gz file.

Oh, and the problem is intermittent. It only happens about 50% of the time!

UPDATE: I restored both database and files backup (4.2.9) and still had the issue even though we had not had issues prior on 4.2.9! I was able to finally stabilize the site by disabling the following extensions:

• GuidedTours (4.3.0 only)
• EmailCloak
• Content Contacts
• Content Fields
• Content Finder
  Then, I re-upgraded to 4.3.0 (extensions still disabled). This was on a very simple site, so thankfully we are not requiring any of those, best I can tell.

UPDATE TWO: Updating to Joomla 4.3.1 did not appear to help.

The error still exists in Joomla 4.3.1:
Failed to open the required file '/plugins/authentication/joomla/joomla.php'.

Are there any further advices?

UPDATE: I restored both database and files backup (4.2.9) and still had the issue even though we had not had issues prior on 4.2.9! I was able to finally stabilize the site by disabling the following extensions:

Probably nothing new: Some servers have a messy backup process. They do not delete the files beforehand, but only overwrite them. In this case, with this difficulty, you have to delete the data manually beforehand and then restore the backup (I also had to do this).

Some servers have a messy backup process. They do not delete the files beforehand

You were on the right track. Not to hijack this thread, but I found the problem for my site:

The website is on a load balanced pair of servers. One site is rsync'd to the other--except for the two cache directories. So, the secondary server needed to have it's cache dirs (or perhaps just the autoload file) cleared out to resolve the errors. This also explains why we were only seeing the issue about 50% of the time. Should have known!

Is there any news about this case?

Same issue "Class "Joomla\Plugin\Authentication\Cookie\Extension\Cookie" not found" here still after restore with kickstart!!

Still no solution?

I have found my mistake. It was a plugin for authentication that has been outdated since Joomla 4.3. I just rewrote it and everything works.
Apparently, however, the error described by @pklinke is still open, but no longer occurs with me.

I will therefore leave the ticket open.

since the issue reported at beginning of this thread, has been solved, i'm closing this issue, and ask to open a proper and detailed new issue for those that still have the problem