What notice? Seems this is not the complet error message

Trying to access array offset on value of type null in line 148 of libraries\src\Installer\InstallerScript.php

Cannot be reproduced, once the installation is done.

Hmm can you add a debugger here:
https://github.com/joomla/joomla-cms/blob/4.0-dev/libraries/src/Installer/InstallerScript.php#L147-L148

And check what is in the $manifest variable? Maybe a var_dump ?

I have to set up a clean installation, as this happens only once. The problem seems to be the manifest cache.

sounds like a valid issue so we need to take care of that and check wehether the old version is set. On a new install this can never be the case. So an if check should do the trick i guess.

I can reproduce this on staging. Happens with extensions that can be discovered (files exist but extension is not installed).

To reproduce:

1. Download Patch Tester.
2. Drop files from admin folder of the package to administrator/components/com_patchtester.
3. Install Patch Tester.

Ok so this should be fixed in staging with the if check mention above right

Closing here is a PR for staging that should than be merged up to 4.x; #29207