This took place in a ~646 LP EUW Master game. For added context, Yunara by this point was 6/2/3 with 181 CS. Darius is 3 items, Qiyana is 2 items, and Ezreal is 1 item.
I counted the amount of healing frame by frame and Yunara healed at least 1,688 HP throughout the course of this fight, almost as much as her full HP bar which was 1,823 HP. Her HP dropped down to a low of 599 HP. 1 second later she's back up to 940 HP, and only half a second later she's already back up to 1324 HP, despite all 4 people still being alive and having been focusing her up until that moment (Qiyana and Zilean then start running).
The different sources of healing she received included, but were not necessarily limited to, Summoner Heal (~278 HP), Mikael's Blessing (~202 HP), Yuumi ult (seems to be ~150 HP per wave? Can't really tell), Yuumi passive, Yuumi's Font of Life, Yuumi's W passive, Legend: Bloodline (fully stacked, so 6.75% lifesteal), Gluttonous Greaves starting at 7 stacks (8.2% omnivamp), Doran's Bow's 1.5% omnivamp, and Triumph (healed 285 HP).
After Yunara had her stun cleansed by Mikael's, besides Yuumi ult (+ potentially Aery and Dream Maker) she was the only person dealing any damage to the enemies for a full 3 seconds since Jayce was first stunned by Qiyana ult then Zilean double Q. At the moment her stun was cleansed, Ezreal had 1300 HP, Zilean had 1100 HP, Qiyana had 1700 HP, and Darius had 2600 HP. By the time Jayce finally gets unstunned and hits a champion 3 seconds later, only Darius remains with ~1000 HP, meaning Yunara dealt approximately ~5700 damage in 3 seconds. If she received full healing from all of her damage she would have lifestole around ~937 HP total, but since some of it was ability damage so didn't benefit from lifesteal, and some of it may have counted as AoE so only had 1/3rd effectiveness, it's probably a safer bet to assume she lifestole somewhere between 500-800 HP, not counting Yuumi's W passive.
I also counted the total damage blocked by shields and it seemed to amount to ~783. Yunara's Barrier was up to shielding 333 damage by level 12, Yuumi E + Yuumi ult shield seemed to amount to ~459 damage blocked (some of that included Aery) Aery claims 211 damage blocked, and Dream Maker claims 46 damage blocked. If you add up the total amount of shielding and healing, Yunara seemed to be working with an added HP pool of around ~2,471, on top of her actual 1,823 HP. In order to kill Yunara within this clip as it played out, the enemy team would have needed to deal a total of 4,294 damage to her!
Some more fun facts!
Yunara started the clip with Grievous Wounds applied to her from Zilean's Oblivion Orb, their only source of anti-heal, which procced from his Aery on the one auto-attack he landed on her before going into passive. This likely denied some healing from Yuumi ult (it claims ~257 healing denied, but I think some of this is counting healing "denied" while Yunara was already full HP, so I'm not sure it actually did deny that much), but unfortunately it got cleansed by Mikael's right as it was about to time out anyway, and therefore did nothing for the barrage of healing that commenced thereafter. With his Aery on CD, he would have needed to hit Yunara with his double bomb to reapply it but he went for Jayce instead, while Yunara was just barely out of range for the explosion (the stun alone also probably would have meant that Yunara died very quickly anyway, with no ability to self-heal with her lifesteal). Had Grievous Wounds been at play, this clip may not have played out so favourably for us.
Ardent Censer claims ~499 damage dealt in this clip, and this seems to be post-mitigation as far as I can tell, so it's likely not even inflated by pre-mitigation numbers.
Yunara's Lethal Tempo dealt 275 on-hit damage in this clip. It had done 701 on-hit damage up until then.
Yunara's Coup de Grace did 532 damage. It had done 931 damage in the whole game up until then.
By the way, I don't have a point in posting this. I have no qualms with the state of healing/shielding in the game, or Yuumi or Yunara or anything like that.
There was a lot that had to go right for us (namely Yunara only getting hit by 1 hard CC which was insta cleansed + no one applying Grievous Wounds, as well as 2 insanely healing champs being paired together to survive long enough for this to happen) so I don't think it's insanely unbalanced. I just think this was one of the craziest moments I've ever experienced in-game and wanted to share it!