No
While the Pathfinder Second Edition Remaster Project does include various changes to some of the original rules, it's not described as a new edition and doesn't warrant a new tag for applicable questions and answers. Instead, reprinted rules should be treated as any other errata for a system and addressed contextually based on the specific question/answer.
To quote the game's publisher Paizo's blog on the subject:
Today, we are pleased to reveal the Pathfinder Second Edition Remaster Project, four new hardcover rulebooks that offer a fresh entry point to the Pathfinder Second Edition roleplaying game! The first two books, Pathfinder Player Core and Pathfinder GM Core, release this November, with Pathfinder Monster Core (March 2024) and Pathfinder Player Core 2 (July 2024) completing the remastered presentation of Pathfinder’s core rules. The new rulebooks are compatible with existing Pathfinder Second Edition products, incorporating comprehensive errata and rules updates as well as some of the best additions from later books into new, easy-to-access volumes with streamlined presentations inspired by years of player feedback.
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Is this a new edition of Pathfinder?
No. The Pathfinder Second Edition Remaster Project does not change the fundamental core system design of Pathfinder. Small improvements and cosmetic changes appear throughout, but outside of a few minor changes in terminology, the changes are not anywhere substantive enough to be considered a new edition. We like Pathfinder Second Edition. You like Pathfinder Second Edition. This is a remastered version of the original, not a new version altogether.
This is distinct from the case with D&D 3.5 as an update to D&D 3.0, where the new books were marketed as version 3.5 of the rules. "Remaster" is never even mentioned in the new Pathfinder Player Core or GM Core books outside of a credited "Remaster Development Team".
Having a new tag for the remastered rules might become confusing because of this, with future Pathfinder 2e readers not knowing their books are updated versions of original books wholly replaced:
In time, the Pathfinder Player Core, Pathfinder GM Core, Pathfinder Monster Core, and Pathfinder Player Core 2 will replace the Pathfinder Core Rulebook, Gamemastery Guide, Bestiary, and Advanced Player’s Guide, which Paizo will not reprint once their current print runs expire. Existing Pathfinder players should be assured that the core rules system remains the same, and the overwhelming majority of the rules themselves will not change. Your existing books are still valid. The newly formatted books consolidate key information in a unified place—for example, Pathfinder Player Core will collect all the important rules for each of its featured classes in one volume rather than spreading out key information between the Core Rulebook and the Advanced Player’s Guide.