It clears on its own, it is harmless, and four days of soaking was nowhere near enough — which is the useful part, because it tells you what to expect.
What you are seeing is tannins leaching out of the wood. How long it runs depends on the type and size of the piece and how dense it is: a small piece of a light, porous wood might be done in a few weeks, a big dense piece can release visibly for months. Three weeks in is early.
Things it actually does:
- Lowers pH slightly and softens water a little. Usually small in a tank with normal water changes, and worth knowing rather than worrying about.
- Absorbs a bit of light, which is the only real effect on plants. In a low-tech ten gallon this is marginal, but if you have anything light-hungry at the substrate it is a factor.
- Nothing harmful. Fish from tannin-stained water actively prefer it.
To speed it up: water changes are the honest answer, and they work in proportion to how much you change. Boiling the wood before it goes in pulls a lot out quickly and also helps it sink — soaking cold barely touches it, which is why your four days did so little. Repeated boils with fresh water each time is the fast route, but that means taking it out, which you said you would rather not do.