Upgrade your storage. 160GB is nothing and 1TB SSDs are cheap
You could delete pictures, but then the posts are broken
You could archive old pictures. The pictures will have a longer load-time. Also I don't think archiving pictures is a feature of lemmy, so you would have to implement it yourself
Edit: I think postgres is so big, because of backups. You could delete those, but that's risky
Since I currently use Hetzner the only way to get more space is to upgrade the server (at a not inconsiderable cost).
The alternative might be to purchase SSD block storage volumes which are definitely lower priced (5€ per month for 100GB) however it would be interesting to know if there is a guide for Lemmy for this or if others have had positive experience doing this.
Since this problem I think is quite common (at least from reading a few threads and comments around) it might be interesting to create a guide especially regarding the part of having lemmy use this/mounted volume instead of the default one.
I in the meantime will try to look around for some information on how this can be done, any advice is definitely welcome.