The frame is 4130 Chromoly and the Chainstay/Dropout is naturally spaced like this. Would I be able to get this welded? If so, beside making sure the welder has experience with bicycle frames, is there anything else to keep in mind?

Appears to me the dropout is broken where it slips into the chainstay.
*If* a replacement dropout could be obtained, perhaps a framebuilder could replace it.

To me looks like that thing had been broken for a while, did not snap out of the blue and just after months of years just gave up.

A lot of heat, drop the old parts, and BRAZE the new one in. Done.

No idea what bike is but if its an old touring frame will be cheaper to get a new one because those dont worth time or money unless was used by EM, it is a one of a kind frame or maybe your grandma used it in the war and there is a sentimental attachment with the frame.

Good luck.

It broke late february of this year during a ride, the frame is a 1986 schwinn world sport.

As already mentioned, replacing the dropout would be the ideal repair.
As second best, heat until the brazing lets go, remove the parts left in the frame. Repair dropout by welding separately. Reinstall in frame by brazing. Welding the cracked piece still in place may lead to the weld being contaminated by the braze material, which is unlikely to lead to a successful repair.
As a third priority, braze the crack with the same technique/material used to secure the dropout to the frame.

Maybe a good TIG-welder would be able to weld the crack w/o contaminating the seam, but I wouldn't tackle it.

Seriously I would recommend hitting on the "Frame Builders Sources" and buy a set of rear dropouts that are close in shape and appearance to the current ones. They give frame and the parts to a frame builder in your area and ask him to do the deed. If you only only replace one dropout, there is a good chance that it might be a little bit off from the other one. Better to just do it right from the start. And it really isn't a huge repair if done by someone with experience in the art.

Your bike is worth around $150. The frame builder in my area who lists repair prices on his website charges $95 to replace one rear dropout. Unless it has sentimental value to you, it's time for a new bike, or at least a new frame.

Yes, it's the dropout that is broken, not the chainstay. A replacement dropout need not be identical to the original in order to be functional. This is a relatively easy repair, particularly if you are not too concerned about cosmetic issues like matching dropouts and perfect paint.

+1 There are frames worth repairing but this isn't one of them unless, as noted, it has tremendous sentimental value to you. That $95 quoted above probably doesn't cover repainting the heat damaged sections of the seat and chain stays either, assuming a paint match can even be found. Cut your losses and camp on Craigslist for a much newer, better replacement for not a lot more than the repair would cost.

A skilled welder can properly prepare, fixture, and weld the dropout as long as there's enough gap to the braze joint to the stay. Otherwise, and possibly the better choice is to braze a new dropout in place, but this is a more involved job, because it means reworking the seatstay also.

Depending on the value of the frame, and the qualified opinion of who you see to weld it, I'd probably opt for the weld vs the braze repair, since there'll be less heat affected area needing repainting.

Either way, have a frame builder or someone familiar with frame repair do the work, since a wuality repair depends on proper locating the dropout so the wheel sits correctly.

Not being mean but is just a touch of reality, to get that fix will be like 200 bucks tops... just because builders hourly rate is like 100 bucks plus materials and a new set of drop outs... that whole bike is like 150 bucks. Unless you know somebody able to braze or tig that thing for free or for like 50 bucks I would start trying to find another one right away.