You don’t need to remove old kernel versions, Rocky will do that for you.
It looks like something went wrong with the graphics driver, could be that your driver was tied to a specific kernel version.
Did you try uninstalling, and then re-installing Chrome?
If it’s a production server, the o/s will be on it’s own disk or on it’s own partition, and a re-install from scratch has already been tested, plus all the data is backed up and in a safe place using open standards formats, so it can be restored to “anywhere” it’s needed. If any of that isn’t true, it’s probably time for a re-think.
At this point, it’s unlikely you’ve lost any data. The issue is that you can’t use the machine from the GUI.
Here are some ideas:
Try to make it work again, by back-tracking over what caused the GUI to stop working. This would be great, but might not be possible.
Work out if you can access the broken computer from a working computer over the network, e.g. can you ssh into it from a different machine? If you can, it’s fairly easy to copy from one to the other.
Can you use a USB stick with the broken machine. I’m guessing you can’t copy and paste text from it, because you’re in a huge text based console? If you can get a USB stick working, you’d be able to run commands and pipe the results into text files which you could then post on here.
If you’ve got a lot of unallocated disk space on the broken machine, you may be able to do a new Rocky install, with new volumes, without overwriting any of the volumes where your data is stored. Even with limited disk space you may be able to “re-format” the volumes that don’t hold your data, but this is getting into high risk.
If you can answer 1-4, it should help others on the forum to give some guidance on the next steps.
Once you have solved the much bigger issues around GDM / login to the GUI, you could probably try to start Chrome in safe mode (meaning: disabling all addons/extensions/plugins, whatever it’s called and if that is possible) to see if it makes a difference.
But I go along with @gerry666uk in suspecting the graphics driver to have an issue with the newer kernel, not specifically with your attempts to remove old kernel files.
Before installing a new kernel, you should uninstall privative graphic drivers or modules from kernel and then install a new kernel without uninstalling old kernel. I suggest you to install again the default kernel. Installed modules are linked to default or current kernel. If you remove, something are missing, that’s the error…