This a recent problem for me as well - not sure it is limited to products that I hold as Draft before flipping the switch to Active.
Same experience as OP reports:
Product Status = Active
Online Store indicator = solid green, but a link below for “schedule availability”.
If I click the link and schedule for the soonest time, like in 5 minutes, the indicator goes half green, but “schedule availability” link goes away, replaced by a link for “Manage”. After the scheduled time has passed, indicator goes back to solid green, and “schedule availablity” reappears.