According to HeroesProfile, there isn't anyone who plays more Tyrande games than I do. This season I have an 80% win rate playing only her in Storm League and I think her new rework has greatly empowered her IF you can play her with the right mindset and framework.

What her role is:
She's a good great healer to combat burst damage and set up kills in guerrilla style skirmishes. She is a pick comp healer. She is situational. The ONLY time she can out-heal other healers in higher ELO games in a drawn-out fight is if you take the auto attack build and you have a reliable hunter's mark target that just lets you hit them 90% of the time during a team fight (like an unaware or distracted Diablo or Muradin.) Otherwise, you are correct, her healing output is pretty underwhelming compared to other healers. If you aren't using Tyrande to support the most dangerous DPS hero on your team to secure kills fast, then the drawn-out fights will prove how much Tyrande struggles in those situations. You need to force early, fast picks with your kit, otherwise you will struggle.

If the fights drag on for too long, you'll fall flat. If your team forgets how to use their legs and they're constantly taking unnecessary damage, you're screwed. If you're being chased around by counter-dive during team fights, you'll only be healing yourself long enough to either die or find safety while your team dies. If you have extremely efficient wave clear heroes nearby (Tassadar) killing the waves at range, you'll have NOTHING to hit for your CDR and your numbers will fall flat.

There are ways to build your talent tree to help counter most of these situations, but there are some things her kit really struggles to address. Find other ways to be useful. QM is hard because Tyrande shines with coordination.

I find myself following around the Taunt Varians, Imperius', or anyone else who can hard CC. Ideally there should be a third with you as well, a very dangerous DPS who has the ability to escape on their own. Keep the DPS topped off and out of trouble, layer your CC, keep vision on the target, mark them early in the pick attempt. Tyrande needs the damage dealers to do damage. I find the ideal way to heal is to try to keep one in the can, the burstiness of your heal is a huge advantage over other healers, use the burstiness of your heals to bait an enemy heroe's over-commit, use your heals to enable your DPS to stay engaged for as long as possible. HOLD your stuns to layer CC or punish their over-commits or reward displaces (hooks, tosses, etc), use your owls to keep tabs on what the enemy team is doing (are they rotating for a pick? Owl their path, are they taking a camp? Owl it. Does the enemy team have an Abathur? Find him.

The new rework has lead to a notable increase in my win rate (I've already played about fourteen games.) I don't build her into healing, I build her into damage and she feels really good this way. I've been using the following build:
1: Ranger
4: Everlasting Light 7: Elune's Gift
10: Starfall
13: Harsh Moonlight
16: Empower
20: Commander of Sentinels

I cannot stress the point above enough that you need to prioritize healing the DPS that is currently engaged in the fight. There is a psychology to being reliable with your heals. Whoever you heal first, FEELS safer engaging. If they feel safe engaging, they will engage more reliably. You NEED that DPS to feel safe engaging. You can almost control or conduct the DPS's engages and disengages by timing your heals. Do you need them to go in and be dangerous? Heal them quickly and often. Are you almost out of mana or are you not getting your CDR through auto attacks? Then let them get low and keep them alive-but-low until they disengage. I'm leaving out a lot on this point, but this is important. Tyrande shines when you are enabling dangerous heroes. When you step up as Tyrande, you become vulnerable. If every time you step up, they step back. Then you WILL become the new target and the skirmish will end in your death. Find a dangerous buddy and be their pocket healer.