The bug
When I have kill a pillager, I've had a bad omen effect but no times is indicated.
Linked issues
relates to 1
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Comments 14
In both cases, the timer shows up as "**:**". Given that Mining Fatigue has been this way for 4/5 years, it's safe to assume that this is Works as Intended. And Bad Omen being very long is just the developers trying to replicate a "permanent" effect.
See also: MC-141723
The effect appears to be unlimited but is in fact limited. It only lasts 1:40:00. That's 1 hour 40 minutes in-game.
So I think this bug report incorrectly classifies the bug. There is a bug with the timer not showing not the effect itself.
Now fixed with MC-121865.
That is the case for Mining Fatigue as well, which is intended. This is just meant to replicate "permanent" effects.