I don't believe there are issues of that kind (academy cards not being marked as academy), the issue with Redirect you reported was that count was 0 with academy core set selected, but from the data I have that it seems Redirect is only available in warlock expansion so that doesn't seem to be a bug (unless my data is wrong). If you have a card count for each set I can cross check that.
I'm not sure I follow.
These cards don't appear under "Useable" but do appear under "All" but still can't be added to an Academy book. For example, your spellbookbuilder says I own 6 copies of Redirect, but when I'm on a slot for an Academy mage (e.g. Beastmaster), the spell cost is "n/a" just as it is for any Arena-only spell, and nothing happens when I click the "+" despite having non-zero card count owned. Same is true for Eye of Bael (of which I own 4 according to the builder).
Are only Academy core set spells allowed when building an Academy mage book?
(I don't have card counts for each expansion on hand, but the count doesn't seem to be the problem)