I'm trying to install a T-connector to this valve but it looks like the hose isn't removable, although I'm not sure. Can someone take a look and verify?
NO, the tubing is part of the valve and not a seperate removeable piece. These valves were common (because they were cheap) a few decades ago. I have seen many where the tubing broke where it is connected to the valve, causing a suprise flood; be careful messing with it.
If you need to tee the line you will need to do it a different way. I recommend soldering a male pipe thread adapter directly to the copper, then using a threaded tee.
If there is no wrench flats it’s not removable. Remove valve and replace they are only 10 bucks. Remove valve, solder tee to existing then replace valve with new or chance using existing.