Centralize the template type resolution logic

Bug: 330885075
Change-Id: I5b3080f730b28a80791554a4c4e48156213ae8df
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5376633


Reviewed-by: Andres Ricardo Perez <andresrperez@chromium.org>
Commit-Queue: Jean-Philippe Gravel <jpgravel@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1282136}