Having actually looked in to this now with a bit more detail than "google it to check your understanding and look at the first result":
It appears you're right, and "fast" is derived from faest while steadfast is a combination of steade and... fast.
Fast friends is a perfectly cromulent phrase :)
The "fast friends" etymological discussion is a non sequitur.
The flaw in this particular part of the HN mindset is looking at a set of information and thinking you can instantly identify the other person's problem (or that there is one!) and explain/solve it using what you already know.
I think other people might recognize this in their own thinking sometimes too!
I think that's fine, as long as you learn to back down and reconsider the moment someone presents competing information.
People trying to explain the origin of the phrase “fast friends” point to the word “steadfast” as an example of where this sense of fast persists. You might also notice the same meaning in our words fasten, colorfast, etc.