IMO the worst flooring for a basement is carpet even a tiny leak makes the carpet stink and I think to try to choose anything but white for the walls will end up being wrong. Remove the carpet get nice vinyl plank in a color you like then choose a wall color. I would replace the flourescents with pot lights with LEDs in 4000K for sure in a basement. I also would not block one window with an AC Drop ceilings are really easy to do LEDs in 3" pots .

Your picture didn't come through, OP. Without seeing the space, I'd suggest a not-too-warm white (e.g. BM's Cloud White) but keep in mind that white will pick up the colours from its surroundings so chances are good, it'll be blue-tinged in spots, depending on light (time of day). A light greige you might consider is BM's Silver Satin. It reads "white" but it's a nice neutral that looks good with blues.

Patricia, when the OP clearly states: "with existing (cannot be replaced right now) carpet", why start by suggesting they replace the flooring?

Thank you both! I’ve looked up the Cloud White and done some further reading on undertones which helped clear things up a bit for me on what’s happening. The bulb suggestion is helpful too - I had no idea where to start.

Patricia I’m with you on the flooring. I’d love to change the carpet (and ceiling and more) but this is my parents house. Our family business is directly tied to Broadway, which isn’t looking so hot and will probably remain that way till at the earliest spring of next year. In the meantime I’m privileged enough to be able to ride out the storm with them, living here, and the paint is a quick freshen up of my new temporary digs. None of us are ready to invest in a big project like flooring until we know what the future of our industry (and our income) looks like. But, in a perfect world, I’d have had the carpet gone before moving in :)

I’ve attached a photo of the offending (really, it’s old basement classic bad) carpet in case it helps. The real answer is probably it won’t matter what color I go with, the carpet is the culprit and I’ll need to grin and bear it.

I think Silver Satin would look good with that carpet, OP. Another idea is paint matching those carpet colours with an app like SW's Color Snap. Could serve as a jumping off point to get wall colour suggestions. But don't forget the furnishings. Wall colour is usually the last element chosen in a room.

I'm sure you'll find a way to make these temporary digs more than palatable for yourself, OP. In any case, I wish you the best as you navigate this storm.