That's the seat stay? Looks like the chainstay at the BB. Anything can be rewelded or splinted and rewelded. If it is the seat stay, then it should be OK because it is under compression. A Chainstay would possibly require some patching as well. Could get tight depending on what else is happening in that space. Other options are tube replacements. I don't know what people charge for that, but it is non-trivial, and I would have thought unless the frame is exceptional it would not be worth it.

Ti welding is a specialty, so you need to find someone who would be able to do it on bike tubes, won't be against doing it, and won't have their time taken up already, and works cheaply, preferably locally.

There is also the question of what broke it, and what else was cranked up in the process.