How can I cover grout lines and gaps against cabinetry and base trim?
Since this looks like a kitchen, the easiest route is to buy some trim (toenail, or quarter round) and nail that to the baseboard (goes faster with a nail gun and some 2.5" nails). Paint it white first, fill the nail holes, and goodbye wall gaps. Add some white caulk to the top to hide the seam.

For a bathroom I would spend a bit more and install vinyl quarter round (won't rot if it gets water trapped).

If nailing isn't your thing, could do it with construction adhesive, but you'll have to full demo the stuff if you ever want to replace the flooring.