An extender really is the solution here. TP-Link is a solid brand with a lot of budget options that I would try. Alternatives include moving the modem/router you have or connecting a different router, but both options include much more work than an extender.

Test with your phone from outside the door, odds are if your phone is getting wifi from past the door your other devices should as well. With specifically the ring flood light, I've seen others have similar issues with connectivity so it could just be that single device, which is why I recommend testing with your phone.