The power you can get is limited by the fact that you're using a 125V / 15A feed. This limits you to no more than about 1200 watts (80% of 15A @ 125V.) That's about the power handling capability of the transformer too.
Compare that figure to 30V at 100A, or 15V at 200A: 3000W, well over what that socket can deliver.
Related: https://diy.stackexchange.com/questions/72733/what-is-the-maximum-load-for-each-of-the-standard-us-120v-electrical-outlets#72734
Then there’s the transformer. Even if you had a larger feed, the transformer couldn't take it since that sort of load is beyond its working range.
Typical transformer welders on the other hand use a 30A/240V feed. With over 6kW available that feed can easily handle the welder power demand.
In short, doing what you propose will pop your breaker frustratingly often, while not getting enough heat to your arc to get the job done.
Can you do this hack for spot welding? Sure. Induction heating? Yes. Arc welding? Nope.
Maybe useful: a short primer on welder power.
MORE: 125V welders do exist. These are rated at 140A or so. However, these are inverter types so are much more efficient than transformer welders.