Magic potions, auras and alien-elf magic buffs!
Seriously now, as I understand from the gritty and dark atmosphere in Cyberpunk, and translating it to digital media, healing would happen in stages:
1) Stop bleeding. For most characters, you get shot, you run.
- For poor / starting characters, first aid would be based on bandages, alcohol, even an old and dirty newspaper to cover the holes while you find a way to be out of trouble;
- More rich characters could have access to better equipment, to stop the bleeding faster, there could be aid-packs, stimpacks, etc-packs;
- Cyberware does not bleed, but could have some sort of malfunction or leaking, then disabling the gadget is necessary;
1.1) Dealing with the pain. The wounds hurt and can impair the character on some skills (can't determine how it would work for now, though);
2) Start the healing:
- Depending on the player's aquisition power, either the forementioned Trauma Team, medication or sleeping through the days. While I agree that it should not be instant, recovery to a acceptable point (60%, 70%, 80%, whatever) should not take much time IRL, spending 30 minutes to 1 hour looking at a screen waiting you character heal is not fun at all;
- Mechanical limbs and gadgets ust be repaired, that's for sure. It's expensive, either pay or live without it (could buy cheaper, used substitutes from black market or junk piles, but would't work so well);
3) Full recovery:
- Not so common, actually would be rare moments when your character is full health, unless you are a bigger shark (an top rank officer, a rich newsperson, etc). Character would need a vip contract with the Trauma Team thing (I don't know how it works on the original pnp game), organ transplant are astronomically expensive to do legally (so, opting in for go shopping new organs in the black market would expose the player again to danger and gang pacts, etc). Buy new cyberware if damaged, spend some time healing at a clinic if affordable;
- Damaged cyberware could be sold to informal tech savvy people, from where poorer cyberwared people would have to buy them;
Damage would also imply in new possible paths to complete objectives and also more danger. Some people would just like to beat you up, because you are more fragile. Otherwise, a more shameless and "acting" character would try to get favours from someone, just because he/she's sick. Some corporate guy would walk up to you and offer to cure you, but only if accept getting your hands dirty in some business. And the ideas goes on...