A single piece of 3/16" has a tensile strength of a minimum of 36,000 PSI.
Follow through the calc.
Tensile strength is force over cross section.
You're assuming A36 steel so then, yes, minimum yield is 36 ksi.
To use this you need to know area. A 3/16" thick bar that is perhaps 2" wide would then be 0.1875" x 2" = 0.375 square inches cross section.
So in tension this example will have a material yield of 0.1875 sq-in x 36,000 lbf/sq-in = 13,500 lbf.
This doesn't mean that this hypothetical recovery point strength is 13,500 lbf. That is going to depend on fasteners, how many and how big are the holes for bolts and shackles, how well the force is spread, etc. Just gives you a material starting point. In this hypothetical the 2" wide bar I picked from thin air is probably not a good choice, with a 3/4" hole in the middle it's going to be suspect.
Weak point will definitely be at the welds.
The wire we're mostly using is ER70S-6, which is 58ksi yield, 70ksi ultimate minimum. It's as-welded strength is going to depend on the shielding gas but if you're using 75/25 it's typically able to achieve about 65 ksi yield and 85 ksi ultimate.
The filler is significantly stronger than the base metal if you're using A36.
That said you are fine to assume the weld is the weak point for lots of reasons. Workmanship, heat affected zone, geometry, contamination. But that isn't necessarily so based on material or process.
Completely agree still, *definitely* prefer to see recovery points that pass through and do not rely on welds. There are fewer unknowns when you see a hunk of continuous steel bolted to the frame.