You have practiced recognizing which technique a problem needs. Subtree queries use Euler Tour. Path queries without updates use LCA. Path queries with updates use HLD. Path counting uses Centroid. Merging subtree data uses Small-to-Large. The insight is reading the problem statement carefully.
Look for clues: "subtree," "path," "update," "count," "merge." Each word points to a different technique. Next section: beyond trees, into graph algorithms starting with connectivity and cuts.