Can't Transfer Data from iPhone 6s to iPhone 13 mini ("Calculating Category Sizes" hangs)

Upgrading to a new phone and trying to transfer all my contacts and app data over to the new phone. Old phone is a 6s on iOS 15.5.

Every avenue I've tried seems to fail:

• Transferring data directly between phones hangs ( at "preparing transfer")
• Trying to backup the 6s to iTunes on my PC hangs (no status I could find)
• Trying to backup the 6s to iCloud on the WiFi hangs (hangs at "Estimating Time Remaining")

In order to get this to work, I've removed all the photos from my 6s and iCloud in order to minimize the amount of data to bring over -- there shouldn't be too much being taken up in storage at all.

In debugging this, I've realize what probably is the root cause for everything freezing is that during storage, "Calculating Category Sizes" hangs, which is probably the root cause. To fix this, I've tried:

• Updating to iOS 15.7.2 which is the latest update available for me -- this hangs when "preparing update" is 90% done, maybe for the same reason that "Calculating Category Sizes" hangs.
• Forcing a Reset by pressing the home button and the side button
• Going into settings and going up to the "Reset data" screen, waiting 10 seconds, and then opening storage again.

Been at it for about 2 days after work -- at this point I'd be happy to just transfer all of my contacts and iMessage info and be done with it...

Any help greatly appreciated!