Yes, the beta did end up getting delayed--on New Years Eve, Meyaoi posted this tweet: https://twitter.com/meyaoigames/status/1344742608560562176
saying that she wouldn't be able to make the original beta 1 release date and she conducted a poll asking fans whether we'd prefer a delayed but complete release (includes all festivals, side quests, cooking mechanics, etc.) OR if we'd like an on-time release that was missing elements that she'd add in as time went. The overwhelming response was "Delayed but complete, please" 😅
As for when we should now expect the beta 1 release, Meyaoi hasn't said. I personally am going to guess sometime this summer, (ie: maybe June or July), but it could very well be sooner or later than that.
Basically, I'd suggest following Meyaoi's twitter https://twitter.com/meyaoigames (whether you have an account or not) as she posts updates on her progress fairly regularly there, so that way you'll for-sure be up-to-date on news as it happens 😉👍