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.
The last time I checked postgres gets big becouse of a log activity table used for deduplication, it stores the data of 6 months. The devs mentioned you could be deleting it up to some point (IIRC they said 3 months, but confirm first).
As for pictrs, lemmy caches a lot of stuff, so it copies a lot of data from other instances even when it's advertised only media from your instance is stored in your server.
My solution was to disable pictrs since I don't upload media.
Other solutions I've heard about are to ask users of your instance to upload media to any other media hosting service, the images uploaded to lemmy are just seen as urls, so it wouldn't be any different.