The solution is getting a wavelength or dark fiber to the off-site, or throwing out the piece of junk SAN that only works on L2, it's too old by now.
The reason I'm very against even discussing this is because people who don't understand the downsides would be open to doing this, shooting themselves in the foot along the way. People who understand the pitfalls just won't and are telling you DON'T, YOUR FOOT WILL HURT.
You could use VXLAN over WireGuard with a lower MTU, attach the VXLAN interfaces to different VRFs and route traffic, it's a somewhat valid usecase.
Switching over the internet is pain, I've got experience. Used to work at an MSP that did this as common procedure, worked fine until it didn't, and noone could explain why. And we're not even talking loops yet, you'll have to build a pretty sick RSTP.
The use-case is at best an SMB migration strategy.
If the post mentioned the pitfalls it would be a fun experiment. But people don't have to ruin a billion dollar company to do damage, hopefully billion dollar companies can afford staff that knows this is wrong, not every SMB can.
Bridging L2 is not the optimal solution for either of your scenarios.