Ello, long time player, finally made an account to report a bug.
These were all tested with a Rexys, as that is the tome I have, would not be surprised at all if they apply to the other two tomes.
Axe shifting tomes don't take many, if any upgrades applied into their shifted form or at least act like they don't in some aspects.
Debug says my SWA drops by 32 from shifting into an axe when it should be going up from two-handed, this may or may not be true as Riagiri and basic attacks still do more damage as an axe.
The burn lv applied by spirit trip goes down to 8 and its damage drops as though the tome was un-upgraded.
If enchanted with Giant Gene, the +1 range doesn't apply to the shifted form
Damage comparison, tome first, followed by axe
Axe damage and burn LV
Tome damage and burn LV
No +1 Range
Debug says SWA drop
If any more information would be helpful please let me know.
I know this was specifically made for the axe tome, but as I said I would not be surprised if the other two weapon tomes had the same issues, if anyone could help me confirm that, it would be much appreciated.
EDIT TO ADD: Spirit axe also does not pierce and hit everything in the line like the skill says it does. Stops on the first enemy hit.