...(I try to help because I find interesting some problems users report, and I learn in the process if I don't know previously the exact solution... And I believe in a human cooperative way to achieve knowledge).
OK. We know the situation a little better now.
Often not well described: your bt devices ALSO have "info" or some kind of data in their guts. When pairing your satechi or roli, they grab some kind of id of device they have been paired to. The satechi keyboard "remembers" up to three connected devices, I believe. I'm not a tech savvy, but I'm curious, and info and implications about this detail is not well studied in the web... There's some info the keyboard keeps !
What if the id or profile of iMac have slightly changed? The keyboard thinks it's connected to iMac, iMac knows about keyboard... but connection is not working. Reseting this data in device is done, usually (and all info stubbornly points to this) from hosting machine: this is, "forgetting" device and repairing from bluetooth preference panel.
But if SO has changed, perhaps it CAN'T completely erase or rebuild data IN the keyboard. I think this is not a trivial problem, and find it interesting. (I hope my poor English don't make me misunderstood; this is a subtle kind of problem).
There should be a way to RESET the device itself (but I think it's not frequently implemented; running out of battery perhaps isn't enough) , and "its memories" from prior connected machines. The "memory" of your Satechi is perfectly functional with your MacBook, BUT perhaps (it has to be this) something has changed in your iMac, BUT nor keyboard nor mac REALISE this fact.
I would try strategies with this in mind. Perhaps there's a way, key combo or something, tho make KEYBOARD forget its settings. If not, perhaps overwriting "1-2-3" connections TO ERASE "old" iMac profile, IN KEYBOARD.
Same for Roli Lumi (and this is a special bt connection).
I think my explanation fits with issue reported by you, and could happen to others, me included. This "small", subtle problems with bluetooth are not well explored and divulged by experts, so is to us (users) to make educated guesses, I presume.
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