That scenario moves the goalpost towards a losing proposition.
You have two important and urgent things and already know you fail at least one of them.
TFA is about non urgent important tasks that you want to show incremental progress on.
If there are multiple of those then those short bursts of works actual work can be eaten up by context switching, reprioritization, scheduling, etc.
What I do in those cases of to arbitrarily pick an order to do those things. (Likeliness to become urgent in the future, difficulty, unpleasantness, etc...) If I can't, I just pick a random order
TFA is about non urgent important tasks that you want to show incremental progress on. If there are multiple of those then those short bursts of works actual work can be eaten up by context switching, reprioritization, scheduling, etc.