As the owner of a welding and machine shop I've had considerable experience with welding thin-walled tubing, 4130 aircraft structures etc.
The OP indicated there was 'some beading' visible inside the tube. Generally a repair of this type is done with another short piece of tube inserted inside the two parts to be joined. Then when the welding is done it is easy to assure 100% penetration throughout the cross-section of the tube. If the weld is done without a place for the root pass . . . and if the inside of the tubing is not purged with an inert gas . . . you will be left with a decarburized area, surface roughness, and a possible place for failure.
The difference between a weld with two pieces of tubing butted together [with the outside bead removed as in the OP's example] and virtually all the other welds on a steel frame is that most of the welds are fillet welds . . . with considerable filler metal remaining to reinforce the welded area.
The welding shop may have done an excellent job on the repair. However, considering the importance of the repaired part . . . I'd opt for a new fork.
DON