Boot into Recovery Mode again and run Disk Utility First Aid again, but this time run First Aid on the hidden Container. Within Disk Utility you may need to click "View" and select "Show All Devices" before the hidden Container appears on the left pane of Disk Utility. Run First Aid on the hidden Container which contains your "Macintosh HD" and "Macintosh HD - Data" volumes...by running First Aid on the Container it will also scan all the other APFS volumes within that Container.
Even if First Aid says everything is "Ok", click "Show Details" and scroll back through the report to see if any unfixed errors are reported. If there are any unfixed errors listed, then you will need to erase the Mac and reinstall macOS followed by restoring from a backup (this process destroys all data on the SSD).
If there are no errors listed, then you will need to free up some space on the internal boot drive, otherwise you will need to perform a clean install of macOS which will destroy all data on the laptop. The easiest solution is to install macOS to an external USB 3 SSD, then boot the laptop from the external SSD. This way you can access the data on the internal SSD to delete or move some files to external media in order to free up enough space (at least 45GB free) to attempt to reinstall macOS over top of itself. This can also give you the opportunity to backup any important files if you don't already have a good backup. You will need to be careful and only use Disk Utility to erase the external USB3 SSD when preparing the external drive for macOS. The whole physical external drive needs to be erased as GUID partition and APFS (top option) before installer can see the external drive as a destination for Ventura.