When using Bobby in multiplayer, I get less than half the frame rate I would in the same area in singleplayer (I am using 32 render distance). With shaders I'm getting less than 20fps in MP whereas I would easily get 80-100 in SP. Without shaders I will get around 150-200fps in MP and over 500fps in SP.
When I use the server render distance (12), MP actually performs better (1000fps in MP, 850 in SP).

The performance with bobby gets worse the more you move around, especially with an elytra, but is still really bad even standing still. With shaders, even If i play on 14-16 chunks the performance gets a lot worse when flying/moving around. As soon as I go back down to server view-distance all is fine.

I'm sorry if the post comes off a bit vague. I'm not sure what other info I can give but I'll include some screenshots.
I also apologize for bringing this up if its an expected thing with bobby. (assuming there must be some sort of overhead? Idk)

Screenshots with shaders. (32 Render Distance)

Screenshots without shaders. (32 Render Distance)

MP and SP screenshots at 12 view distance with no shaders (Multiplayer actually gets more here for whatever reason)

This is my current modlist for testing. I made this instance for testing and found bobby was causing the lag (i'm pretty dang sure anyway)

Please re-take these screenshots without BetterF3, it removes Bobby's debug info and as such makes it harder to reason about what exactly is going on (and some of its values also just seem flat out wrong, like Chunk Sections total is at 24 in all screenshots).
As another point of comparison, please add a third scenario which is SP but with viewDistanceOverwrite in Bobby's config set to 12 (that should act like the server but without a separate server process). Note that you need to re-enter the world for this is apply.

You can skip the shader scenario if the issue is obvious without shaders as well, in that case adding shader just complicates it. Ideally also remove all other mods, keeping only sodium and bobby for now, to further simplify the setup.

Please also be careful to use the exact same position and rotation for all screenshots and wait until all chunks have finished building, so the different scenarios are as close as possible. The video is barely useful because in MP you're way up in the sky (when the F3 screen is open) where it ofc has to render a lot more chunks because you can see a lot more, and it's not even done building them so performance may greatly fluctuate because of that too.

https://www.youtube.com/watch?v=YNE_YKVAmUc

This will better show how it is on Singleplayer vs Multiplayer.
It usually starts off sorta fine, but once all the chunks get loaded in it's almost unplayable :(

Ok, I apologize for not providing much helpful info.. I wasn't aware what exactly you needed from the screenshots (I was mainly just showing how bad the fps gets, and praying there was maybe something useful lol).

I'll exclude the shaders then. I was showing how unplayable it gets with them in MP. (Its less noticeable with no shaders when it dips to 150-200fps, but definitely is noticable when it tanks to 20fps with shaders in MP)

I'll follow your advice and give an update soon, hopefully.

Sorry again for providing useless data.

where update

edit: i also experience this issue

i use 127 chunks (for screenshots) on a superflat survival server and the difference is small (like 4 fps)

I'm having this issue too. I'm dropping from 80-160 to 40-90.