I play Thousand-Tailed Watcher on my turn. My opponent is on combat with my Bilgewater Tracker. If my opponent uses Decree of Focus on his unit, does my opponent get +4 might for the unit, or does it get +1 might only?

No — as described, your opponent can't legally play Decree of Focus there at all, so the question of +4 vs. +1 never comes up: it needs a friendly unit "in combat with an enemy Fury unit," and Bilgewater Tracker is a Body unit. Watcher's ability doesn't choose anything, so the "being chosen by an enemy Fury spell" clause doesn't cover it either — no legal target, no buff.

If the unit it was fighting were Fury, your opponent would get the full +4, not +1. Watcher's −3 is its own modifier that already landed on the unit; Decree's +4 is added on top rather than being whittled down by it. So a unit that was 4+ Might when the trigger resolved reads −3 then +4 (a net +1 versus its original Might), but that's two separate effects, not Decree being reduced to +1.

One wrinkle: because the −3 is snapshotted against "to a minimum of 1" when it applies (Rule 479.4.b), a unit at 3 Might or less took less than −3 at the time — e.g. a 3-Might unit only dropped to 1 — so a later Decree still moves it up a full 4 from wherever it sat.