Challenging, but not impossible to clean. I would extend the countertop to the edge of the wood "backsplash"

If you extend the countertop on only 1 side the entire piece will look off center. Stay with the 1 inch overhang. How do you plan to finsh the wall behind the vanity?

Stay with 1” overhang. Otherwise it will not look right. A Swiffer duster will clean that side space. A hand towel hanging on right side wall not too high will distract the eye from the gap.

I would remove that wood back panel and put matching countertop backsplash on this piece. Water and wood not a good combination.

Just a 1" overhang. Don''t extend the top to the wall. And I agree that it is too wide for the space but cleaning between the vanity & the wall is small potatoes compared to cleaning underneath and all of the detailed mouldings, carvings, recesses, etc. on the vanity itself.

That's a freestanding piece so, no, you shouldn't extend the top to the wall. If the cabinet was designed to fit that space, there would be a filler piece in the corner at which point you could abut the wall with the countertop.