How Much Input Lag Is Actually Normal, And Is My Controller Too Slow?

Your readings are healthy, and the reason the forum advice contradicts itself is that people quote different things as though they were the same number.

What a browser test measures is the time between the controller's electrical event and the page receiving it: the controller's own polling interval plus the transport plus the browser's event loop. It does not include your monitor, your game engine, or your own reaction time. Published figures like 5ms usually come from lab rigs measuring only the controller's radio and polling, and figures like 50ms are usually whole-chain measurements from button to pixel. Both can be accurate about different things, and neither is comparable to what you just measured.

For the measurement you actually took, these are the practical bands. Wired: 8 to 15ms is normal and good, 15 to 25ms is acceptable, above 25ms is worth investigating. Bluetooth: 15 to 25ms is normal, 25 to 40ms is acceptable, above 40ms is worth investigating. An Xbox Wireless Adapter typically sits between the two. So you are comfortably in the good band on both.

For fighting games, the number that matters more than the average is the consistency. A pad that is always 19ms is far easier to play on than one that averages 14ms but swings between 8 and 30, because your timing adapts to a stable delay and cannot adapt to a variable one. Run the test for a minute or two and watch the spread rather than a single figure. If your spread is tight, stay wired for tournaments for the extra few milliseconds and otherwise stop worrying, because you do not have a problem to fix.