I, too, upgraded to a 2018 MBP a week ago and have been having Magic Mouse V1 issues exactly as you two have described. Frequent disconnects, error -3903 (peer doesn't exsit [sic]) error messages, and no change after battery swap, paper/foil shims, resetting PRAM/SMC/Bluetooth, and resetting the mouse to factory defaults.
However, I've replaced the mouse with the newest version and am still having these issues - same Console pattern, same error messages. In fact, I've seen "Connection Lost/Connected" messages 8 times while typing this message. I'm curious to see if your issues returned in the last two weeks after replacing.
This happens in multiple environments as well, whether I'm in my home office downstairs, or upstairs in the living room, or out of my house. I don't think it's interference.
I had a 2017 MBP before and never had these kinds of issues.
Here's the console log on a disconnect event:
default 09:42:12.737194 -0400 bluetoothd EVENT: DisconnectionComplete
default 09:42:12.737297 -0400 bluetoothd EVENT: Disconnection Complete: Connection Timeout
default 09:42:12.742378 -0400 UserEventAgent [BTUserEventAgentController deviceDestroyed] count = 0 previousCount = 1
default 09:42:12.742423 -0400 UserEventAgent [BTUserEventAgentController deviceDestroyed] seconds of numberConnectedDevices[1] = 63817
default 09:42:12.742460 -0400 UserEventAgent [BTUserEventAgentController messageTracerEventDriven] deviceDestroyed
default 09:42:12.742492 -0400 UserEventAgent [BTUserEventAgentController messageTracerEventDriven]
default 09:42:12.744857 -0400 bluetoothd == IOBluetoothBroadcomSchedulerWorkaround start
default 09:42:12.746319 -0400 bluetoothd USBProductID 0x7B USBVendorID 0x5AC
default 09:42:12.746360 -0400 bluetoothd schedularWorkaroundActive? 0
default 09:42:12.746388 -0400 bluetoothd active? 0
default 09:42:12.746415 -0400 bluetoothd == IOBluetoothBroadcomSchedulerWorkaround end
default 09:42:12.746445 -0400 bluetoothd == IOBluetoothBroadcomSchedulerWorkaround start
error 09:42:12.747126 -0400 AirPlayXPCHelper Dave Werner's Mouse has no service mask
default 09:42:12.747720 -0400 bluetoothd USBProductID 0x7B USBVendorID 0x5AC
default 09:42:12.747762 -0400 bluetoothd schedularWorkaroundActive? 0
default 09:42:12.747818 -0400 bluetoothd active? 0
default 09:42:12.748041 -0400 bluetoothd == IOBluetoothBroadcomSchedulerWorkaround end
default 09:42:12.748168 -0400 bluetoothd ***** [BluetoothHCIEventNotificationMessage] kBluetoothHCIEventDisconnectionComplete
default 09:42:12.749539 -0400 UserEventAgent [BTUserEventAgentController messageTracerEventDriven] PowerSource -2.000000 -2.000000
default 09:42:12.749587 -0400 UserEventAgent [BTUserEventAgentController messageTracerEventDriven] SystemState 0xE0000300 0xE0000300
default 09:42:12.749626 -0400 UserEventAgent [BTUserEventAgentController messageTracerEventDriven] LidStatus 1 1
default 09:42:12.749657 -0400 bluetoothd Apple HID device count: 0
default 09:42:12.749659 -0400 UserEventAgent [BTUserEventAgentController messageTracerEventDriven] BluetoothState 1 1
default 09:42:12.749733 -0400 bluetoothd updateAppleHIDConnectionIntervals - connectedAppleDevices 0
default 09:42:12.749693 -0400 UserEventAgent [BTUserEventAgentController messageTracerEventDriven] StateApple80211 4 4
default 09:42:12.749774 -0400 bluetoothd updateAppleHIDConnectionIntervals - twoSniffAttemptDeviceCount 0
default 09:42:12.749726 -0400 UserEventAgent [BTUserEventAgentController messageTracerEventDriven] FlagsApple80211 0x00000008 0x00000008
default 09:42:12.749813 -0400 bluetoothd updateAppleHIDConnectionIntervals - connectedSCODeviceCount 0
default 09:42:12.749760 -0400 UserEventAgent [BTUserEventAgentController messageTracerEventDriven] ConnectedDevices 1 0
default 09:42:12.749796 -0400 UserEventAgent [BTUserEventAgentController messageTracerEventDriven] ConnectedDeviceTypes 0x0000000B 0x00000000
default 09:42:12.749828 -0400 UserEventAgent [BTUserEventAgentController messageTracerEventDriven] update to latest event information
error 09:42:12.753050 -0400 bluetoothd Apple80211Get(APPLE80211_IOC_BTCOEX_MODE) returned error -3903
Looking for any additional insight or anything anyone else has tried. Getting work done is nearly impossible.