iPhone SE unable to fully pair to Apple Watch Series 3/Watch won't update

As the title says, I'm having trouble getting the pairing/update process to work for the Apple Watch Series 3 (and iPhone Se). Upon pairing my iPhone SE to the Series 3 Apple Watch (via "Start Pairing" and either typing the 6 digit code or using the camera to find the watch), I'm greeted with the message of having to Update my watch to 5.3.7 if I want to be able to pair my Watch to the phone, where the other option is to Exit Setup and Start Over. So, I tap "Update Now" which leads to it saying that it's checking for updates, before it ultimately gives the message "Unable to Check for Update - Checking for a software update failed because you are not connected to the Internet." I am absolutely connected to the Internet. The options are to Start Over or Try Again. Try Again obviously doesn't do anything, and Start Over simply unpairs the two devices and I'm back to square one.

Things I have tried/things that I am making sure to do:

• "Start Over" option, at least 5 times over
• Resetting both devices at least 5 times over, as well as one or the other multiple times
• Turning off and on Airplane mode
• Resetting the Internet connection
• Turning off cellular data
• Connecting to a different Internet connection
• Disconnecting from internet connection (ie using cellular data only)
• The Apple Watch IS connected to the charger
• The iPhone IS connected to the charger
• The Apple Watch shows up in Bluetooth on the new iPhone, and does not on the old one

I upgraded from an iPhone 6s, so I actually still have the 6s (it was unpaired from this device automatically; when I synced my iPhone SE via iTunes, it asked if I wanted to unpair from the 6s to instead pair to the new phone, to which I said "yes" which started this debacle). I have tried putting the SIM card back in the iPhone 6s, then attempting again to pair the watch to the 6s, and it simply tells me something along the lines of "You cannot pair the Apple Watch to this device," which I find frustratingly hilarious since it was literally just paired to it hours ago before I got the new SE. Now, I have a hunk of glass, metal, and rubber that can't even tell the time because it is stuck in "factory reset" mode (when half-paired, it shows the apple logo in the middle of a circular green design with the specs of the watch on the outside of the design) since I've reset it to try to get it to work, and it can't even pair back to my old iPhone.

Please please please, if anyone has any idea why this is happening, or if this is a known problem that will be fixed in the future, let me know. Thank you!