rending toward moderation encourages extremism and obstructionism, because you get more leverage on the center from the edges.

No, you don’t. What you’re thinking of is a consequence of runoff elections (including instant runoff) that doesn’t apply to preference voting. Preference voting functionally works to blunt the extremes down, unless you have a sufficiently large base radicalized to be you or nothing but then if a majority is dead set on you or nothing that base was going to win regardless of the electoral system.

Have you read Project 2025? As an American, that shit is terrifying, and the idea that we should find a middle ground with Christian nationalists is abhorrent.

Except an approval vote wouldn’t be a vote to find a middle ground on every issue in Project 2025. The idea that Trump or any other Heritage Foundation stooge is a moderate candidate that’s likely to get enough votes to win in an approval vote system where they wouldn’t also win under FPTP or ranked choice or STAR is frankly absurd.