Which vehicles could work for my RV?

Keep in mind that many mid sized and some full sized SUV's have frontal area restrictions along with the weight capacity issues. Most are limited to 32 square feet of frontal area which eliminates most TT's.

I have a 3,500 lbs TT that goes up to 5,000 lbs fully loaded.

I'm pulling 4runer 4WD with it and it's more than sufficient although the SUV is rated for 5,000 lbs.

You should be ok although I would advice to get something that has longer wheelbase.

VS ib516's scenario with 185hp and a 5speed auto, you can get a midsize 6 banger with close to or around 300hp and 8speeds maybe more. Dog will hunt.

If it's really only 2600lbs and not 36 or 46 then I'd say no problem with a midsize. Just take'er easy up hill or into headwinds, the frontal area of the trailer will be working against you pretty hard.
Brakes are not an issue as long as you have good working trailer brakes.

I'd swear that tow ratings are calculated with a tail wind. I wouldn't want to tow that with anything less than a V8 SUV. That gives you a little more weight for stability and power for climbing hills.

I towed a 17' hybrid TT (the one in my signature pic) with a 2007 Pontiac Torrent V6 with a 3500# tow rating. The RV weighed 3500# fully loaded. It did OK, but required my utmost attention, and I only took short local trips on flat terrain.

If your RV weighs 2600#, I am assuming it's about the same size as mine. An SUV like the ones you mention will do the job, but it's not a combo I'd want for long distance towing, windy days, or lots of hills/mountains.

A note on RV weight, no one tows an empty trailer around when camping, so you're best to use a higher weight (like GVWR) to make your calculations on towing combos. For example, the 2615# you mention would be unloaded or dry weight, and 3500# may be the RV's GVWR. Use the 3500# to find a suitable tow vehicle. Just my thoughts.