Will this adventure path be written using the changes from the Remaster project?No.
I finished writing it a few months before the whole OGL situation happened, and it was well into development and layout when those events did happen. The very nature of this adventure has a deep dive into nostalgia, and that includes a fair amount of encounters with OGL-themed monsters that would have been tricky to adjust for... even if we DID have time to go in and make those adjustments at that late stage in the process (which we did not).
You can, of course, run the adventure using the Remastered rules. You'll need to be fluent in both the remastered rules and OGL rules to do so, relying more on the OGL rules for short stat blocks of monsters taken from the Bestiaries and the Core Rulebook for many of the spells those creatures use and for many of the magic items the PCs will discover, but since both are 2nd Edition Pathfinder, it'll work fine. You'll just have to have extra books or additional sites open in your browser is all.
The trickiest part is if your players want to play a wizard with the Runelord archetype. In this case, the best bet is to let that player use the OGL version of the wizard and archetype, as I'm not sure we'll have a Remastered version of that archetype available for folks to use by the time this adventure is out.
I'm looking into the possibility of providing more advice for folks who want to run it using the remastered rules, but we're VERY busy at this point and it might end up being limited to me giving out said advice here on the boards or over on the Pathfinder 2E reddit forum, etc.
Thank you for clarifying this! I was wondering the same thing.