alt Hacker NewsProgrammable qubit is almost certainly referring to one where gates can be applied, non-error-corrected. The error correction overhead would be much larger than 4-to-1.
Although note, the above is if you are referring to error correction in the traditional sense of error correcting codes. According to Ars Technica's article [1], the non-programmable qubits are being used for leakage removal: coupling to the computational/programmable qubits and stabilizing them, but not being used for any computation themselves. This is far from error correcting codes in the mathematical sense, but it does have a similar purpose of reducing noise.
For what you are wondering about in your penultimate sentence is possible for any algorithms, I am not sure, but it's a very good question. However, I know that for general algorithms, there is a range of error reduction techniques you can use short of full QEC, IBM has a decent blog post about them [2]. Usually, the trade-off is error reduction vs increased number of shots and post-processing (so vs time, not space).
[1] https://arstechnica.com/science/2026/11/ibm-to-offer-access-...