They achieved an actual logical qubit for over a millisecond using error correction? Please correct me if I am wrong, but isn't this a huge breakthrough relative to previous progress?

My understanding of quantum computers hit a brick wall some time back, so please correct any errors:

Shor's algorithm requires not only the logical qubit to be stable (the superposition of 1 and 0, but also the phase -- in the remaining dimensions of the bloch sphere) of the qubit to be noise free to an extraordinary degree. There are rotations in very small angles many, many times in the computation.

This QEC algorithm trades phase for increase stability in the logical qubit.

So, if this QEC is used, doesn't that imply the resulting system could not execute Shor's algorithm. Could it be that it forgoes many of the algorithms that enable "quantum supremacy"?

Edit: Maybe I should have said real/imaginary parts of the Qubit? QEC seems to only worry about the real part, and trades the imaginary to keep the real stable?

"In this work, we used real-time error correction to real- ize a fully stabilized logical qubit whose lifetime is more than doubled compared to the best passive qubit encod- ing in the system, marking the transition of QEC from proof-of-principle studies to a practical tool for enhancing quantum memories."