All single transistor circuits are going to invert the phase. Though it only matters in a parallel or stereo rig.
I have not been marking circuits as inverting or non-inverting for a very long time so just because it is not marked doesn’t mean anything. Nobody ever seemed that interested. If a circuit is actually marked one way or the other in the shop then it is correct.
The NostalgiTone Ascension Boost uses a single transistor stage so it does invert the phase. Alternatively, the NostalgiTone Preamp Boost uses a non-inverting opamp so it does not. Also a reason to provide more than one type of Boost.
You can peruse some common circuits already listed here: https://www.thegearpage.net/board/index.php?threads/list-the-pedals-that-invert-phase.796444/
This is a Guide from our Guides Page:
https://guitarpcb.com/wp-content/uploads/2018/08/PHASE-FOLLIES-A-Phase-Inversion-Guide.pdf