A single Zero-fill, will take data below the recovery potential of any available user tools - in fact, probably already to the level that only forensic recovery is possible.
Modern PRML data channels are much closer to the threshold than the old “peak response”.
Any of the popular free tools should place the data in a condition where attempted recovery requires a LAB.
The main exception to low level format, being that some drives may not fully implement it.
I’d suggest eraser or DBAN, maybe also (or instead), a “data destructive” test from the drive maker, and then if you want to be really sure that it was well covered, format the drive and copy something unimportant over it - clipart, shareware archive discs etc. then delete or reformat (carelessly).
I’d consider a vital step of a secure erase, is to make the result look completely uninteresting.
The finer points, do depend on your requirement to put the data beyond “normal” recovery … which ONE overwrite most certainly does achieve, or beyond the most expensive recovery.
If I gave you a single erased drive, and you were not allowed to open the casing, I’d be confident you’d get nothing out of it.
To rehash, a lot of the old magnetic media erase patterns were designed for simpler encodings like MFM, and were designed to target any uncertainty around the transitions. other patterns were designed to resolve to lower or higher frequencies, and in modern ARLL encodings, will not resolve the same way.
I see Gutmann targets 3 ecodings, MFM, RLL (2,7) and RLL (1,7) - not sure if modern drives use encodings beyond 1,7.
The point is, that the advanced erasure is targeted at the traces that cannot actually be read by the drive itself, and there is a very big difference between the data being gone from the drive (as the drive sees it), and totally obliterated.
An example - do you use a paper shredder, and if so, is it a strip cut or a crosscut, or do you burn documents you want destroyed.