But apparently not completely - Adam and Eve didn’t become all-knowing (at least, there’s no indication of that in the story) - they simply gained some measure of knowledge. It wouldn’t be discordant with that for the Tree of Life to grant a partial effect as well.
It may be worth noting that the Tree of Life in Revelation (a book saturated with references to the OT, so it could very well reflect the Genesis Tree of Life was thought of in the first century AD) is said to bear fruit continuously, on a monthly basis, and it is said that its leaves are for “the healing of the nations”. Now, that certainly isn’t inconsistent with a “eat it once, permanently gain eternal life” function, but to me it suggests that it is meant to be eaten on a continual basis.
All of this quibbling over how the Tree of Life worked is probably missing the point, however, since (as @deuteroKJ mentioned) themes throughout the Pentateuch and the rest of Scripture make it plausible that the tree symbolized access to God’s presence and thus to the source of all life himself.