macOS

I want to backup my Mac onto my ssd drive so that I can safely upgrade to Mac OS sonoma beta, but time machine gives the error message that the disk doesn't have enough free space. I always thought that time machine automatically deletes older backups when it runs out of space, but it appears that it doesn't. I searched for tutorials on how to delete backups but none of them seem to work for the time machine interface on Mac OS ventura (most of them involve clicking a gear on the finder window in time machine but on my mac there's no gear icon). Any ideas how should I do that?