@Mark-k 

I think it may be keeping the same exact SSID. I know for convenience you wanted to keep it all the same, but given the issue you are seeing I would create a new SSID. Another way to test that would be to enable your guest network and make that a different SSID, and have some devices connect to that (ex. testwifi). If that resolves it then you can change the SSID on your main network and connect everything back.

@Tony What do you mean by keeping the exact same SSID? Isn't that what I want? I kept the SSID from the old router, at least I kept the name the same.

I'll enable my guest network and see if that works. What is the difference in functionality between a guest network and the primary network?

@Mark-k 

Keeping the same SSID is what you want, but I am thinking about what to change or try to see if it resolves the devices having trouble connecting.

Using the guest will mean devices on the guest network will not be able to talk to devices on the main network. For example, hosting a media server where other devices on your network connect to locally. If you do not do any hosting or sharing files from one device to another and just simply get internet access that should work fine.