It depends on whether or not you think the act of distributing is part of the commonly understood definition of canon.
The definition most reasonable Trek fans operate on is "the shows and movies made by the rights holders," although most aren't aware they've internalized that second part because nobody wants to admit they spend any amount of time caring about "the rights." (Ask them if they think Continues or New Voyages is canon and you'll cut to the heart of that matter real quick.) That latent "rights holders" qualification isn't there out of any particular deference to Paramount, it just gives us a convenient and durable boundary that a huge, varied, and global fanbase can largely agree on. Paramount decides what Star Trek to produce, but that decision results in canon Star Trek because it's a simple enough boundary for Trekkies to collectively accept without much friction.
Point being, Paramount is part of the definition but Paramount is not the source of authority for the definition. The fans are. This is an important distinction if you want to investigate whether or not this ugly Prodigy business has altered or clarified the definition of canon.
This act of cancelling and archiving is uncharted territory, yes. Assuming you agree with my earlier definition, it comes down to whether or not you think there are more qualifiers hiding after the word "made." Something like "made, released, and currently being distributed," which is an interesting set of qualifiers to add because it would decanonize pre-remaster TOS.
Personally, I think that's too much control over the definition to hand to Paramount. We care about "made" because it's the most minimal way to establish this "rights holders" boundary. I think we could have a reasonable debate over whether or not "released" is already part of the intuitively understood definition (i.e. "are deleted scenes canon?") but I would wager most Trekkies will agree that "currently being distributed" is not part of the intuitively understood definition.
So, yes. Prodigy is still canon.