Can't update reactive value from download handler

[bhu]

When attempting to update a reactive value from within a download handler, the value is either not updated until modified by another action button:
Shinylive example

Or the value is not updated at all when separately registering a side effect:
Shinylive example

Is this the intended behavior (implicit asynchrony for the download handler)? Or would there be a way to properly modify reactive values from within download handlers?