[Extensions] Separate lazy and non-lazy event dispatch logic

For readability, and in preparation to more complex changes to
non-lazy event dispatch logic.

This CL doesn't introduce any behavior change.

Bug: 439995191
Change-Id: I365aa9ac40646d52837d04fac66bee144539d678
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6908251
Commit-Queue: Andrea Orru <andreaorru@chromium.org>
Reviewed-by: Devlin Cronin <rdevlin.cronin@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1509740}