I have this exact problem on an M1 iMac running Ventura. When the internal storage was reported to be full, I deleted or relocated 60-70GB of files. Within a couple of days the available disk space was back down to a couple hundred MB and once again I was seeing "disk full" messages. Clearing a few more GB and within days if not hours, the full disk returns, the Mail app doesn't open, Time Machine does not back up, and I can't even run the system restore or update.
The suggestions made here aren't really of much use as they are mostly about deleting more files, which we already know does not help, as that space will vanish very quickly. They also don't explain how to use Console to find "overly large" log files. These files are visible in the Finder if you know where to look, but once again it's impossible to know which if any of them are growing "uncontrollably." Deleted log files will also be reinstated by MacOS. So what good this could possibly do to fix this problem is unclear.
The System Settings in Ventura also provide a place to see how much space is being taken up by different types of files, so we really don't need an app for that -- but how do we know what's considered normal? All we know is something has gone haywire in Ventura that causes it to chew up every available MB of storage. What that is, or how to fix it (short of nuking the entire Mac) is what we need to know.