Thanks for the detailed video.
It
could still be your console

What the Super Gameboy does is it doesn't really do any scrolling on the SNES. There's a complete Gameboy on the cartridge itself (which then runs the Gameboy Everdrive). Any scrolling happens inside the Super Gameboy itself, it just copies graphics data from the built-in Gameboy to the SNES. The SNES just shows a static screen setup with the tile graphics getting replaced really fast.
The failures you showed on the Mega Man X games are pretty "high level" though. In addition to not scrolling the background, also the sprite positions aren't updated as they would normally need to be to adjust to the moving background.
My first wild guess would be that either the SNES's internal RAM or the sd2snes's internal RAM is faulty.
I have two suggestions for further testing:
1. Can you find and run the "SNES Burn-in Test Cartridge RevD", specifically "5. BURN-IN TEST" and check the result? Please disable the In-game hook in the sd2snes's configuration menu before running the test because it can cause one of the tighter timing tests to fail.
Note: the test switches between interlaced and progressive video modes a number of times. Depending on your screen the picture might disappear briefly while the screen adapts to the new resolution.
I found a youtube video (not made by me) that shows what the full test run should look like:
https://www.youtube.com/watch?v=HA6CQ3Lr1do2. The sd2snes diagnostic firmware should be able to give any clues about a possible sd2snes malfunction:
https://sd2snes.de/blog/cool-stuff/sd2snes-diagnostics