While I didn't check if they have champagne at the MH regional lounge post-refurb, I know it had bubbly before the refurb, so I'd expect it to remain that way. Don't expect anything fancy, though.

If for some reason they don't have it and you really want your champagne, you can still head to the CX lounge by taking the train. It's not much of a detour because you'll have to board the train at some point to reach your boarding gate.