We found that they worked, it was just that the Internet was slower than it could be. The choke point turned out to be the old Linksys and not the modem or ISP.
A switch would be just for cat5 or cat6. For the phone you want 2.4 (older devices) and 5G wifi. My understanding is that you have already run a cat 5e or cat6 cable between one of the LAN ports on the ATT modem/router combo to the garage. That got your full network speed to the garage. cat5e or cat6 is generally good for up to 300' +/-. What you need really is wifi in the garage, and the ability to add more cat5e or cat6 cables there to any computers you put out there. Let me see if that router has an access point only mode which will remove the router and any slowdowns. What happens is that the router has to change the address on everything coming in from the old network to the new network. Imagine if your mail carrier had readdress everything sent to you because you changed you house number before he/she could put it in the mailbox. Then change the from address too on everything sent out. Most of the data (TCP) that gets sent has a header in it, and the data. As that data is sent the device receiving it has to acknowledge every packet of data or the sending device sends it again, assuming it has been lost in transit. The translation to another network in both directions slows things. When you are getting something that streams - it usually uses UDP. That protocol does not rely on a return from the device saying I got it. So if a packet gets lost the device simply skips over it. That is Ok for music or streaming, but in a file that relies on it being perfect it has to use TCP to be sure all the packets are received. Ever go to a webpage that is slow and times out? The packets get lost or corrupted on the way so eventually the receiving computer says I'm done waiting.
