The photos are taken too close up to help the reader understand the overall problem including all the places there are gaps between the vanity and the walls.

Apologies for bad pics. is this better? To clarify, the gap is from the top of the vanity to the wall. 72 inch long vanity. 1/2 inch gap all the way lengthwise. Usually this gap is dealt with just caulking. However, 1/2 inch is a very large gap to deal with just caulking alone.

I think I’d give shims a try first.

The best option is a new top; it will template to the wall and they can add small over hang on sides to help cover the open space at the vanity sides.

i think maybe adjust the legs on the front if possible. Looks like the entire vanity is just tilted away from the wall (or the wall is just off of plumb?). If it was leaning back a tad, it may rest fully against the back wall.

Check. the floor and vanity are level and plumb. it's the wall that is not!

honestly, even if the floor and vanity are plumb, I'd see what it looks like if you shim up the front. if it's only tilted back a few degrees you might not even notice the angle, but the gap will be a million times better. you should at least consider it and take a look!

Don't invest in a new top. Shimming ought to do it. Walls are often not straight and not plumb; which is one reason custom cabinets are worth waiting for.