I have a post just before yours about the same problem that confounded me for weeks after I tried setting up my newly repaired watch. I'm happy to report that after considerable sleuthing I have my watch able to consistently connect remotely to my phone (i.e. WITHOUT Bluetooth).
The problem was two-fold:
#1: Since the repair involved replacement of the watch's main pcb, the built-in e-sim number changes (called the ICCID which can be found in the watch's ABOUT menu). Therefore my cell service provider tech support had to update my line to the new ICCID. That reestablished data service to the watch's new e-sim.
#2-The default value for the data limit in the watch's "Connection/Data Usage/Data Limit" menu is 0. It ignores that until you change something like the start date for your data in the "Connection/Data Usage/Start Date" menu. At that point the watch reports a brief warning that data service is unavailable until the next billing cycle because the data has been exceeded (since it's still set at the default value of 0!).
The fix to restore data service for item #2 is quite simple. Via the watch's "Connection/Data Usage/Data Limit" menu, increase the limit to 100 GB (the max value allowed) with the dial. Your data connection is now NOT exceeding your monthly data allowed, restoring your data connection, and therefore your remotely connected watch when NOT using Bluetooth.
I hope this works for you as it did for me. Basically I think it was an oversight of software (a bug) that hopefully will be addressed SOON for all those still experiencing problems with getting the remotely connected function to work.
Unfortunately #1 is not applicable to my situation as i have not had a repair, and #2 did not resolve the situation.
Thank you for your suggestion though a better attempt than Samsung seem to have made.
I recently purchased a Samsung Galaxy Watch 42" LTE. I bought this specifically so that I could use it as a standalone device.
My watch will not switch automatically to remote connection mode at all and if I connect to it from the Galaxy Wear app, it disconnects within a few seconds, or, as soon as I try to do anything. I have tried this on both LTE and Wifi mode. The LTE connection and Wifi connection are both working fine for accessing the internet.
If I turn the bluetooth on my phone off, or move away from it, it switches to standalone mode.
I have done a factory reset on the watch and cleared the data and reinstalled the app on my phone (Huawei P30 Pro) and the problem persists.
Please advise urgently Samsung, as this device is basically useless to me without this functionality and I am now paying a monthly fee to my service provider for the LTE subscription.
Yes, it appeared remote connection was down on Saturday and Sunday and finally came back up yesterday. This is the third time in like 6 weeks it has been down. Samsung needs to get off their rear ends and fix this instead of telling people to do factory resets as they have no effect on a systemic issues like this.