I am running Windows 11.
The PC is assigned to 1 of 3 in the Easy-Switch. When it loses connectivity the '1' light is no longer lit. Issue is only resolved by powering off the mouse and powering back on.
I have tried:
Charging the mouse overnight
Moved the Logitech Unifying Receiver to different USB ports
Checked for new firmware and updates for Logi Options+
I was having this exact issue for a few days. After trying a number of fixes mostly related to the bluetooth receiver, I realized the issue was most likely within the mouse itself. Changing ports did nothing, and connection was resolved just as yours was, by cycling the power switch on the mouse.
Now, it's likely too late for you (I see you purchased a new mouse) but I believe I've found the solution, and if you ever have this issue again with the new mouse, this may help. I may eat my words if it fails again soon, but it's been functioning for nearly three hours straight now when before I couldn't get it to work for more than 5 minutes, and sometimes only miliseconds.
To anyone else who may find this: The solution appears to be disassembling the mouse and cleaning the switch connection. I cleaned around the power switch connection and along the circuit board with a cotton swab dipped in 99% isopropyl alcohol. Nothing appeared amiss; there was no noticeable debris or corrosion, but it appears to have resolved the issue! It could also have been a poor connection and simply disconnecting/reconnecting everything resolved the issue, but whichever it was, it seems to be a hardware malfunction, not software.
I will say to anyone attempting this: be careful. Make sure you carefully remove the screw covers so as not to deform them, and get all the way underneath them so they you don't strip it off the under layer. I also accidentally snapped one side of the tab connector for one of the ribon cables; those DO NOT come all the way off. Thankfully I only broke one side, and it should hold fine so long as I'm not throwing and banging my mouse around. Also, the screws holding the battery housing are slightly longer than all the other screws. You will also need a tiny star screwdriver for one screw, but the rest are all tiny phillips.
I also may have messed up my left and right mouse buttons just a touch. My left mouse seems to some extra travel now, and the right is finnicky, but I think the last one is mostly because I didn't put in the housing screws yet and it's all just a touch loose. I may pull her back open and try to resolve the button issues, but even if I don't get them just perfect, SHE WORKS, which is far more than I can say before this operation.
Here is a video I found with very detailed disassembly. You only need to get the circuit board out to access the switch on the bottom, but it was very satisfying to watch the entire disassembly process.
Best of luck to you all. I hope this helps someone keep their mouse functional for at least a little longer.
Peace, love, and all that jazz.
~Ellian