Hi Sven.
Even with old SPPB3.x you should be able to see Joomla 4 or Joomla 5 Admin area (backend), so I guess there is something else, old plugin or admin module maybe.
as 1st step: delete all old SPPB modules from folder administrator\modules
In theory you can try to update SPPB files manually ...
If you have access to Template Qucikstarts , take Trove (the last one). Unzip it. Then using FTP upload & override those folders and files from it:
- administrator\components\com_sppagebuilder
- administrator\language\en-GB\en-GB.com_sppagebuilder.ini
- components\com_sppagebuilder
- language\en-GB\en-GB.com_sppagebuilder.ini
- language\en-GB\en-GB.mod_sppagebuilder.ini
- modules\mod_sppagebuilder
- plugins\system\sppagebuilder
then after reinstall component in classic way to update database and update language files.
If you don't have access to Template Quickstart you can upload folders from SPPB package, but it's more tricky.