A Heavens Door anime is at least plausible.
Um… it’s April fools. I can’t tell if some people are joking or not. Do they not see the title?
This has nothing to do with Angel Beats. Summer Pockets is an entirely different production and has no continuity with Angel Beats, which was a straight-to-anime production, unlike this which is a Visual Novel/Game. Stop misinforming people if you want your publication to be taken seriously.
This is an April Fools joke, one that has been going on for 3 years in a row, there’s no one trying to misinform anyone.
If it helps, remember that every announcement on the last day of March or the first day of April (depending on your time) should be considered a April Fools joke until proven otherwise.
FAKE UNTIL PROVEN REAL
That doesn’t mean you can’t join in on the fun though, just don’t get fooled more than once if you can help it.