See summary. Screenshot below shows a level 255 bad omen raid. Raids seem to constantly be occurring, replenishing the "Raid" boss bar.
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See MC-10755.

By "negative levels" I meant levels over 128.
See minecraft.gamepedia.com/Status_effect#Behavior.
"Due to the way this amplifier is stored in NBT, amplifiers of 128 to 255 (levels 129 to 256) in NBT tags (e.g. on potions) are treated as if they were −128 to −1 (levels −127 to 0) respectively. The /effect command
initially applies such amplifiers in their positive-valued sense but this is later converted to the negative-valued interpretation, leading to inconsistent results."

Just wondering, but does Bad Omen's level increase by 1 every time you kill an illager patrol leader? Because I can't figure it out myself due to the very low illager patrol spawn.
Strangely, the bad omen effect seems to be supported up to a level of 9 instead of 4. I found this out by using F3 + I on an illager leader that spawned in a patrol, copying it's data onto a command block, and summoning a bunch. I killed many of them and my bad omen got buffed for every leader killed until it got capped at "Bad Omen IX", which can cause the maximum raid you can get in survival.
Patrols tend to spawn more often as global regional difficulty increases, but they currently never spawn in superflat. See MC-139817.