Is it possible for rendered chunks to be saved somehow so that what you have loaded is not lost when you leave the world. (on a server)

That's exactly what this mod does (unless you set "Cleanup Unused Regions (Days)" to 0, then it'll still save but immediately clean up everything once you disconnect).

@Johni0702 on our Server (Paper) it does not save the chunks, or it does not load after restart, could there be an bug?

allways after rejoin, we need to fly over the chunks again, we had multiple worlds and added the multiworld setting.

Ah, it's probably to do with the multiworld setting then.
For that to work, the mod needs to be able to find a unique match between the world the server sends and one of the worlds it has saved from a previous session.
If it is unable to find a unique match, either because none match or because multiple match, it won't know which one to pick and therefore won't load any (at least until you walk around more and it does find a unique match).
Try running /bobby worlds full to see if there are any worlds and to see how they well they match your current world (unfortunately there isn't currently any way to actually see what's in these worlds, so one can only guess by their size and the amount of chunks matching; I originally didn't bother implementing anything because that's effectively an entire world map mod then, but now that I'm thinking about it, it might not be too difficult actually).

If your worlds are inherently similar, such that the mod is bound to be unable to reliably distinguish them (note the mod only looks at opaque vs non-opaque blocks, it doesn't look at any the specific block type or other data; and it'll ignore chunks which contain little identifying info, such as unmodified superflat world chunks), then it would be best to change the ids or seeds of the worlds on the server, such that the mod no longer has to guess.

It might also help to merge all local worlds together or simply delete the entire .minecraft/.bobby/<server> folder to start fresh in case you got into a situation where the mod incorrectly decided that your current world is not the same as a local world (e.g. because your surroundings were heavily modified while you were offline), then you explored the entire server again, and now you have two local worlds that almost entirely match the server world, so no matter where you log in, the mod will always see two worlds matching the current world and will never be able to pick one.

Hey, we will check this, we had an World, where we can Build our buildings and the 3 farmworlds, to get collect the items.

The buildworld is allways the same and the farmworlds would be allways resettet.

The buildworld should have allways an unique chunk or what did you mean with unique? I think it should have data on our side, that would allways the same as bobby has saved it.

We will check this on our side

After testing, it does only work on 1 from 10 times, dont know how it would be fixed.

Nobody change an chunk, but it need always to load the chunks new

We don't get an check from uniqe chunks, could it be, the unique is broken, if there spawn entities or something? Don't know how it check the chunks...