Great question. You're not the first to ask so perhaps I should make an amendment. Controversially, I'll often avoid tracking health in my role playing games entirely. I like to limit how much players look down at their sheet as much as possible, to make sure they connect with one another, and have a sense of performance freedom with their improv. I usually save the risk of death for later in the story.
That said, The Power Grid is intended to have a bit of a Rock-Paper-Scissors structure; Offensive < Defensive < Tactical < Offensive, and so forth. The attacking character will roll with an Offensive skill and the defending character will have to quell the attack (Combat), or withstand it (Durability). Speed replaces initiative, but you can also make a case for Intelligence with a player who can predict the fight and form a plan. Regarding health and damage, Durability is the Skill you'll want to lean into the most. You can treat this as the amount of hit points a character has, and if an opposing roll supersedes it, then consider that skill temporarily lowered. You can also combine this with Reality to measure their ability to recover, and where to roll death saves when the time is nigh. Quite a bit of time has passed since I ran the game, but there are some examples of this in action during the 20 Sided Stories finale.
Essentially, turn order and moves come from Tactical, with fights being a series of opposing Offensive vs Defensive rolls. In the case of tie rolls, defending always wins, or you can add a personal trait into the mix. At the end of the day though, I see the stats as modular building blocks that purely exist to help players with their role play. For example, I let Eric/Scry use Combat offensively from time to time; he didn't have raw strength but he knew how to deliberately dismantle enemies. Mahsa's powers specifically came from her Personal Traits, so I leaned into those much more for her.
This emotionally-driven style is not for every group, so of course if you find your way to be more satisfactory, fun, or specific, by all means, mod away!