If you have access to a router you can re-laminate the Formica with one of over 5,000 updates styles available from Wilsonart, Pionite, Formica & more.
It will last you up to 30 years, and you’ll be tired of looking at it by then, lol.
This forum is typically about coating things cheaply, and the new plastic laminate itself is cheap, considering it won’t have to be re-done in 5 years- like the Rustoleum Plastic Laminate Coating System.
If you want to see a video on this, I can find one from Formica in it. All plastic laminated are installed with contact cement. Let me know.
You can also paint it if you aren't able to replace it. Here's a tutorial that might help: https://www.bobvila.com/articles/how-to-paint-formica/
Paint it they sell kits for this very purpose. Check out the Amazon.com they carry several to choose from and read customer reviews before ordering to get some inside info on how well they worked.
If you have found a tile you like that is at least 1/4-3/8” thick, and at least 1” wide (length doesn’t matter), then you can apply the tiles as a border all around the sink. If the tiles will have to be cut to size, you will need a tile (ceramic) blade for an electric saw and a tile sander. The measurements I gave are pretty easy to find, although smaller tiles can be used more creatively; they just take more delicate grouting, like with mosaic tiles. Use a waterproof adhesive and grout, and smooth out tiny pores with a toothpick or plastic tool. When the grout is completely dry and cured, add a waterproof sealer. If, during this makeover, you painted the rest of the Formica, make sure that has cured at least two days, also, before you apply the sealer. Then let the sealer cure about two days before setting anything on the countertop. This should last for several years unless someone intentionally scrapes or sands the countertop. Best wishes, Jewell.