Sprocket touching the biggest cog no matter B screw...how do I fix?
Both the TY-300 and TY-500 are rated for a large/low sprocket of 28T to 34T so they are both within spec.   There are no other variants, only the -SGS long cage is available.

https://bike.shimano.com/en-EU/product/component/tourney/RD-TY300-SGS.html

https://bike.shimano.com/en-AU/product/component/tourney/RD-TY500-SGS.html



I'd strongly suggest checking the the hanger alignment before spending more money on replacement parts.

You need a bolt that fits the hanger (possibly salvage this from your old destroyed unit) and a longish flat rigid bar, and something to measure down to the rim.



The measurement of the offset to the rim needs to be as accurate as you can, but within 10mm at the rim should be adequate.



The other option is that your B screw is damaged, bent, not pushing hard enough, or the stop is broken/damaged/missing.  A clear and well-lit photo of your frame and hanger would help show if this is the problem.