Sentence Construction – Correct Use of ‘Has Not Been Coming’ or ‘He Is Not Coming’

There are slight nuances to the different words. Both implicitly place "blame" and the nuance indicates where.

The page has not updated.

This places the "blame" on the page or the system itself. It's pretty neutral. "Oh! the page hasn't updated. We've done what we ought, but the page hasn't kept up."

The page has not been updated.

This places the "blame" on the content administrator. It is a little more apologetic. "Oh! we didn't update this page. It might be that we don't have anything new to say or we just weren't able to get around to it."

Which makes more sense? In the future, this would be a better fit for the UX SE site

Have as you used it, it's the present perfect, where If you use be+-ed you usually form the Passive form.

As you can imagine

is come

doesn't make sense, because that's an active action he does. Instead

Lunch is ready

is ok, because it's something "Lunch" suffers

If you want more detailed information you can check this resource.

I would say:

1. Tea has come
2. Lunch is ready
3. He has come back
4. She is assigned for work