Why are the metal tools scraping off the patina of the wok

As long as the surface isn't rough (i.e. with burned-on bits of food) then yes, the patina should be a dark brown or black.

That's more-or-less what a patina is; it's essentially tarnish, the result of cumulative oxidation, which normally happens to some metals anyway but is accelerated by the rapid oxidation of oils via high heat.

If you end up with a slick, evenly-distributed black layer, then you've seasoned it perfectly. If it's streaky or splotchy then you need to start over by scouring it down.

(P.S. Carbon steel is different from, for example, cast iron, because the latter is porous and you'll never see that perfect black, just a noticeable darkening.)

You have overcooked the seasoning. I have done this once or twice too. Especially smooth surfaces (e.g. carbon steel) are very prone to this problem, unlike rough cast iron.

What you want is not a dark layer. The layer will darken with time and start looking like usual. But on a freshly seasoned metal utensil, the layer should be yellow-brownish. The stove may be too hot for this, especially a gas stove, I do my pans in the oven, for maybe an hour at 200 Celsius or somewhat lower. A burner under thin metal can cause hot spots of much higher local temperature, where the oil chars instead of polymerising.

There is also the type of oil you use. Generally, unsaturated oils polymerise easiest, but the final layer stays somewhat sticky. Saturated fat can give you some more trouble, but will have a smoother finish. I do multiple layers, starting with 1-2 layers of flaxseed oil - this gives a good basis, it is so unsaturated it can practically dry out by itself in the air - and finishing with cocos fat or lard, again 1 or 2 layers. For the first few time in a new pan, I try to fry with saturated fat too, for your wok you will probably find that the taste of cocos fat has a good harmony with Asian dishes.

And a word to the cleaning before: Vinegar was not such a good idea. Woks are made from reactive metals (that's why they need seasoning) and metals react with acid. Using acid to clean naked reactive metal will result in invisibly small pockets of reaction products on the surface of the wok, mostly rust. You can do this as an early step in cleaning, but afterwards you have to use something to make sure you have removed this too. To peel off the seasoning before reseasoning, you are much better off using a base, as it does not react with the metal. This will ensure that the new seasoning sticks to the metal itself and not to impurities which can be dislodged over time.