Marine varnish on painted counter tops?

Yes. This is the best.

or a liquid epoxy -- it's a 2 part product -- like 'bar top' sealer

You may like faux painting but I would hesitate if I were you. Every day looking at it can become tiresome. Also, not that you should care, but faux painting stopped n the 90s. I am sure you are a very creative person and can come up with a better alternative.

Well thank you. I do faux granite on my countertops, which is the latest craze. Also my question was about a sealer. See below

You can but it may need to be redone as it wears away. Also would not be heat or food safe. Use cutting cutting boards. Better to use a countertop paint kit. They are epoxy based and last a long time.