Anyone remember the first Rainbow Six game, or the SWAT games? You didn't need a heath bar or healing in those, one or two shots and your guy was down possibly dead. I think that is how Cyberpunk 2077 should play, at least until you get cyberware.
I think it would be good if the early missions (locations near where you start), are mainly stealth or investigation with few enemy contacts, or at least ones you can surprise and get the drop on. As you get more equipment and/or cyberware the mission present more opportunities to go on a killing spree against corporate goons, but generally there still should be a non-combat way through the missions for people that focused skills in a different direction. No end bosses that your are forced to fight, and you stand no chance against if you haven't decided to go the Solo route (Deus Ex:HR I'm looking at you).
Armour would be the first item you are likely to get that will improve your survivability.
Healing would involve visiting a Ripperdoc, and downtime (during which events happen, look at X-Com for inspiration (but no alien invasion)), and would not be available during a mission unless you had a Med-tech character with you.
Cyberware would greatly improve your survivability, and reduce healing times.
Trauma Team contracts could be used to recover a character that actually dies on a mission.
You don't need a health bar. Even a biomonitor implant should one show your heart rate/blood pressure and give another clue as to your condition.
Your condition would be reflected by changes to game controls, as you get weaker it gets harder to aim, you might limp if shot in the leg, you might be restricted to one handed weapons, if an arm is injured.
So to the initial questions - Health regen or Stimpaks?
Neither. I'll take a dose of realism thanks.
Okay I'll expand that a little. Some health regen with cyberware, but still no health bar. Drugs could negate the some of the pain effects of wounds, but don't stop the visit to the Ripperdoc at the end of a mission, and won't actually heal you to full by magic, or mend that shatter arm.