Wet and dry paper on float glass, does the scary sharp method hold up for kitchen knives or is it a woodworking thing

Do not try to map paper grit onto stone grit, they are different scales and different abrasives and the numbers lie to you. Judge by what the edge is doing instead: are you raising a burr along the full length, has the previous scratch pattern been fully replaced, does the burr flip cleanly. A 2000 grit paper finish on a kitchen knife will slice paper and push cut a tomato happily, which is all a kitchen knife needs.

The catch is consumables. Paper cuts fast when it is fresh and then falls off quickly, especially on the harder steels, so what feels cheap on day one is a sheet or two per session by month three. Stones you flatten and keep. If you are doing three knives to see whether you enjoy this, absolutely use what you already own, that is free information about whether you want the hobby. If the answer turns out to be yes, a single 1000 or 1200 grit stone will do more work than a whole pack of paper and stop the ongoing spend.

It works, and it works better on chisels and plane irons than on knives, for a structural reason. A chisel has a wide flat bevel that sits on the abrasive and registers itself, so the paper cannot do much wrong. A knife bevel is narrow and you are holding the angle freehand while pushing along the edge, and any give in the paper lets the abrasive wrap slightly over the apex and round it. Two fixes: stick the paper down properly with spray adhesive or a wet film of water so it cannot lift, and pull the edge rather than push it into the paper so you are not digging in. Do that and you will get a genuinely sharp kitchen knife off 2000 grit.

First attempt I used the paper dry on bare glass with no adhesive and it slid, bunched under the blade and I put a lovely convex round on the front third of a knife. Took me a long session on a proper stone to grind that back out. Water film under the paper, or tape all four edges, and it behaves.

Fine for German kitchen steel. Stick the paper down, keep the pressure light, finish on the back of an old leather belt. You will not need stones until you buy a knife that deserves them.