When Tibbers deals 3 damage to all battlefield units before combat, does that damage persist until after the next combat or do units heal immediately?

Ruling: Damage dealt outside of combat persists on units until after the next combat or at the end of turn, whichever comes first. Units will be weakened during the next combat.

Nuances:

• When any combat happens on any battlefield, all units across all battlefields and bases heal from damage
• This means you can only fight one battlefield with damaged units before they all heal