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Here’s the code if you’re curious.
Mine runs in 1ms (in rust, single thread) but is fairly complicated (link).
Check mine https://github.com/Fadi88/AoC/blob/master/2021/day19/main.rs Just checking orientation invariant property to get matching sensors and form there calucte rotation
You can calculate the distances between the points found by each scanner. If two scanners report points with the same distance between them, then most probably they are adjacent. Runs in 4ms on my machine: https://github.com/SvetlinZarev/advent-of-code/tree/main/2021/aoc-day-19