Not sensitive at all, it's just a kitchen

Any comments are welcome. I know generally paint is not a good choice but I didn't know if there were paint or paint-like coatings that could be used specifically for countertops. I've tested what's on there with a knife, and you can more or less cut on it without scratching it up. I could of course be wrong but I don't think it's typical wall paint. Which doesn't mean it's not toxic.
As for budget, I would have to say "it depends". For a permanent option I'm willing to spend some money, but if it's more than, say, $500-ish, I can plan for the permanent option in the future but would like a temporary quick fix for now. And personally I hate the look & feel of cheap formica.
Is there any way at all to tile over what's there, such as screwing or gluing down some proper backing? Or I've heard it
might be possible to score the top with a saw blade, and tile over that... There's one corner of the existing countertop that's chipped due to ripping out the backsplash, and it doesn't look like it would be possible to remove the top layer from the backing board. I checked out under the cupboards too, and I don't see any easy way to remove the entire countertop. It's not screwed in for easy access the way they are nowadays - it's pretty solid all around. Which means I'd like to not tear it apart if at all possible.
Definitely planning to keep the cupboards, though we'll paint them white. I really like some of the 50's details on them, like the rounded corners.