If you feel compelled to spend several thousand dollars, replace the counters and buy a new sink and faucet. HGTV is not sending a judge and jury to look at your kitchen. You don’t need to paint the cabinets and tear up your life for six months and spend $50000. My personal opinion is the only reason to totally remodel a kitchen is it doesn’t work for cooking.

Do you know the brand and model of your cabinets? You could replace the upper arches and glass fronts with the doors like you have on the base cabinets and clean up the frou-frou a bit. Quartz counters and a pretty backsplash, along with paint would go a long way. Def level out the peninsula. New pendant lights over the peninsula would be nice, too. The cabinets are very pretty, I would not paint them.

I would keep the lowers as they are BUT I would paint the uppers white. Then do the white counters that you mentioned you would love. Peninsula all at 1 level will you give you much more usable space....so I would rip out that tiny island (if the flooring extends underneath it). = open, airy, "new" kitchen.