I’m confused. Are we talking about the Recorder database (home-assistant_v2.db) being the problem, or the log files? The image in the OP shows what I’d consider a large database, but that depends on what hardware you have available and how comfortable you are with a .db file that big.
@chairstacker, purging the short-term data with the purge action (what used to be called a “service” is now an “action”) will not delete the long-term statistics. In fact there’s no defined way to do that, even if you want to. For that you need to do your own database hammer in SQL while HA is off-line.
A lot has been written here about keeping the recorder database size manageable. This would be a good place to start.