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The rule for AI backup strategem reads:
"Backup AI [1CP] - Epic Deed
Use in your command phase. Select one T’AU EMPIRE model in your army. Until the start of your next command phase, it counts as having full wounds remaining for degradation."

And the rule for Nova charge is:
"Nova Reactor: Can activate in your command phase, if you do roll 2d6, if the result is greater than the riptide’s remaining wounds the nova reactor burns out and cannot be used for the rest of the game."

Can I choose the order in which these activate and us the strat then test for activation and have the benefit of full wounds?

You are quoting it wrong, it says: "Until the start of your next Command phase, that model is considered to have its full wounds remaining for the purposes of determining what characteristics on its profile to use."

I don't think the Nova reactor is a characteristic.

Backup AI specifies that "that model is considered to have its full wounds remaining for the purposes of determining what characteristics on its profile to use".

That has zero interaction with the Nova Reactor.

There is no interaction between these two stratagems. Nova Reactor is not affected by degradation and thus does not benefit from Backup AI.

But is not wounds a characteristic? And as the nova reactor test says to make its tests on remaining wounds but the strategem states to treat characteristics as max wounds so woundn't wounds, being a characteristic, be effected, and count as max wounds for such a test against a characteristic?

“Counts as having full wounds” means they can get e.g. better BS by using high statistics as if they were on top bracket.

It doesn’t in any way actually increase the number of wounds remaining.

So no interaction as such.

This. The two things aren't connected.