Hello, I had an issue with the kernel entries, wen i updated the kernel, the old entries stood in boot screen (I'm using uefi) deleting old entries and updating clr-boot-manager solved the problem, though I had no problems booting with the new installed kernel and I'm not sure if it is persistent.
Note: Solus uses clr-boot-manager as boot manager software and is in charge of it, no matter if it's uefi or mbr. I uSed both.[Please correct me if I'm wrong]
olivir $ sudo clr-boot-manager list-kernels
com.solus-project.current.6.3.12-241
com.solus-project.current.6.3.8-240
$ uname -r
6.3.12-241.current
For what I can see, you have the latest kernel the correct entry and old entries
Set the com.solus-project.current.6.3.12-241
as booted, as you are using it
sudo clr-boot-manager report-booted
Then delete old entries
sudo clr-boot-manager remove-kernel com.solus-project.current.6.3.8-240
finally update
sudo clr-boot-manager update