I'm not sure that you are correct. I've tried to read https://arxiv.org/abs/2306.10072 in the last day and if my reading is right (I am very stretched by this stuff so I am very happy to be corrected) then no amount of error correction will rescue Shor's - only zero error phase gates. I suspect that a similar story is true for native QML, as quantum memory scales it's just going to get exponentially harder to maintain it.

I believe the current record using Shor's algorithm is 31, done by IBM recently.