I’ve moved your post to the Ask the Community section of the forum, since it contains two unrelated comments, and no clear proposal for a new feature.
Auto-fill on page load does require the browser tab to be in focus, so this is known/expected behavior. Here is another thread on that topic:
However, the delay in the automatic auto-fill is not something I can test on my end (because I do not enable auto-fill on page load, for security reasons), so maybe other users will be able to confirm whether or not this behavior is reproducible.