Yes, you are overthinking it. Unless you have been instructed to do so, you need not identify the writing style you are using or find the proper name for it. In my academic writing on the Masters level and for an academic social work journal, no one indicated that this was necessary. However, getting rid of the pronouns might help you clean up your writing. I agree with your observation:
I wrote it as "It is currently unknown if such a derivation exists."
However, I feel this has a meaning of 'nobody knows if it exists'
whereas it's really just me and my supervisors.
As you note, you don't want to speak for the entire academic community when you know only the position of yourself and your supervisors. However, you can "hedge your bets" by delineating the basis on which "It is currently unknown." I assume your statement is based on one or more of the following:
- lectures and the literature of your discipline
- your own studies and/or experimentation
If it is based on the literature, name the authors and their studies, etc. If based on your own studies and/or experimentation, list them. Rephrase your statement along these lines:
Based on [insert your basis], it is currently unknown..."
You also ask whether to use past or present tense, based on what "feels right." If you are going to opt for the traditional writing style where no pronouns are used, you will also want to write in the past tense that goes with it. Present tense for the sake of comfort may have worked fine so far but for the professional polish I think you want to go with past tense. After all, the experiments and studies are now in the past, if you need to justify it to your feelings.