I got my new 2021 Rav4 less than a month ago and only put about 110 miles on it but yesterday I noticed one of the rear wheels is significantly deflated(and almost flat). I only remember a glass bottle cracking in a parking lot but that was 4-5 days ago and didn't really think much about it at the time. I'm new to cars so not sure what I should do at this point. Would I have to buy a completely new tire or is there a way to fix it? Would a portable pump like https://www.amazon.com/gp/product/B07VMM69N9 fix the issue? Or do I take the car to the dealership and would they fix it for free under the 2-year Toyota Care warranty or should I go to a tire shop down the street(I'm in Queens, NYC)? Honestly, I didn't expect to run into trouble this early in my new car and would greatly appreciate advice from experienced drivers/mechanics.
It depends on where the damage to the tire is at whether you'd need to replace the tire. If it is on the side wall, tire places will not fix it. I'd assume (from your description) the damage is most likely in the tread area. You won't know until you get it looked at, though. Tread can most likely be fixed with a patch from the back side, unless the damage is great. Considering it seems like a slow leak, it should be okay to fix.
As far as a pump goes, it's just a stop gap measure. It's not going to fix/solve anything. You'll need to get the tire fixed long term.
It appears the Toyota Care warranty only covers changing out a flat tire for the spare. It doesn't cover road hazards, which if the glass is what has caused your troubles, is what it would be considered.
Any competent tire shop should be able to figure out what's going on with the tire as well as what the solution is going to be to get the car back to golden. If you don't like what they have to say or what they are doing, you can always go to another place and get a 2nd opinion. Just ask them their opinion and their solution and go from there. I never suggest going to the dealership because they usually price gouge on anything they do.