The fingerprinting comes from enumerating properties of the terminal equipment and their values, and to do that you have to read them, for which you need the explicit consent. (Except in some rare cases, but if you are that case, your workplace will also have a legal department.)
Additionally, as you said, GDPR adds a lot of additional restrictions, with provisions regarding creating profiles of persons (what is commonly refered as tracking).
The thing the site is doing that isn’t “strictly necessary” is always tracking.
It also limits the exception in relation to e.g. employment.
So a canvas/font/WebGL fingerprint used for tracking needs the same consent as a tracking cookie. The guidelines even suggest passively collected protocol signals can fall under it (para 43), though that's where it gets argued.
The weak point is enforcement. A cookie shows up in devtools and in every cookie-scanner audit. A fingerprinting script looks like any other analytics JS, so it's much harder for a DPA to spot and prove.