Most of us have been there when an old tub drain basket refuses to come out gracefully.
If it still has the cross bars at the bottom, one could use a tub drain removal tool with a screw driver for leverage and back it out.
If you then break the cross bars or the cross bars have rotted out then you can try one of those “friction fit” wrenches. May be 50/50 chance.
If that doesn’t work, then your only option is to vertically cut a few lines around the drain basket, do it ever so gently to not cut excessively into the threads of the drain shoe, then “peel” the basket out. I am wondering what power tool, if any, do you use to make those cuts.
There isn’t really a fitting power tool for making these vertical cuts. Not a dremel, not an OMT, possibly a super short stroke length reciprocating saw…
I know they sell “retro” adapter baskets that you epoxy into the existing basket, that may work in some situations but raises the lip of the drain by 1/16″ or so. But sometimes it gets to a point where it’s personal between YOU and the DRAIN BASKET.
Try an internal pipe wrench. I would be careful using any power tools to cut the drain out, you take a serious risk of damaging the body of the tub. I’d maybe try a hacksaw or a Sabre saw to get a little more control in the cut.