[DevTools] Make AIDA conversation handler available for new features

Ensure that `doAidaConversation` is not only available when the
console insights feature is enabled, but also as long as any other
relevant feature is enabled.

Bug: 369540372
Change-Id: Ib6a89a0c19e17fbf1ca58e4409264c143a24190e
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5912763
Commit-Queue: Mike West <mkwst@chromium.org>
Reviewed-by: Danil Somsikov <dsv@chromium.org>
Auto-Submit: Wolfgang Beyer <wolfi@chromium.org>
Reviewed-by: Mike West <mkwst@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1368244}