According to the Japanese website, Home's 4.0 update is coming in Spring 2026.
The infographic shows off Champions so, I guess April for that too
The japanese website also has a few, ah, interesting articles
https://news.pokemon-home.com/ja/page/716.html
This one says you send pokemon from home on an "expedition" to Champions (probably a quirk of auto-translate). More relevantly, sending specifically Greninja, Mawile, Eternal Floette and a fourth one i already closed the tab on gets you their mega stones, with notes about how they have to be from Z-A specifically and can currently only be obtained in this way but might become available in the shope later
https://news.pokemon-home.com/ja/page/718.html
And this one, which is giving everyone in Champions a free Dragonite.
And the mega stone is from...the first season's battle pass (might be in the shop later too, from a footnote)
And reconfirmation that no you can't transfer Pokemon from Champions into Home.