WWDC might be the good date to look for (if not in the 2 weeks either side as a press release, but ARM is too big of a deal to press release it on this occasion.
The Mini's
Coffee Lake CPU has been discontinued and last stocks are due to delivery around June 4 time - depending on how Apple stretch it out they might make it last until October which is a traditional hardware announcement month but 4 month lead time is substantial.
The same CPU is employed in the iMac 21.5" which hasn't seen an update since 2019 so it stands to reason that both will be refreshed at the same time.
The iMac seems like a great candidate for a WWDC keynote with the mini hanging on its coat tails as a high end SKU to finish off the mini transition.
If we're discussing the M1X then it could certainly go into a top SKU Mini, 21.5" iMac replacement and then into a 14" and 16" MacBook Pro - especially interesting if Apple start grading versions of M1X with differing numbers of compute cores and GPU cores.
And since Apple aren't releasing MHz figures I'm going to assume that clock speeds will stay consistent across each model, so perhaps we could see M1X in lower power setups while M1Z carries more horsepower.