This is an overview of the new hero, and I'll update this as I learn more.
Her primary is both her heal and her damage-dealing ability (you can only heal or deal damage, not both at the same time). Her heals are on a resource meter that fills up slowly over time, and fills up quickly as you do damage to enemies. Her left click is her heal, and it works like Mei's primary fire does, meaning it requires decent tracking. Her right click is a slight lockon akin to Symm's gun (less lenient meaning you still have to look at them), and has a slightly longer range, however it deals less damage than Winston's primary does. Dealing damage will heal you and refill your heal resource and obviously charges your ult. I'm not sure whether her damage goes through shields like her other abilities do, but I don't think it does
Her teleport which I think is her Shift ability is on a 6 second cooldown. When you use it, you go invisible, and you get to control your movement for a very brief amount of time, during which you go MUCH quicker. It has a slightly longer range than Blink does, and you have better 8-axis control than you get with a Tracer blink, but it only lasts for about a second if not less. During tele, you also turn invincible fo r the short amount of time it lasts.
People are comparing it to Zen orbs, but it's not quite the same. It heals and does damage at the same time (if an enemy is in range of it) You choose between the damaging and healing orb, and bounces off of surfaces, but it does go through barriers. It will heal for 300HP total before disappearing, but if there's no one to heal, it'll bounce indefinitely until it either does the max damage that it can (200HP), or until 300HP is healed. Heals are spread equally amongst everyone in its AOE (including a Moira running alongside it). It moves pretty quick, but requires a decent skillshot to actually be effective with it. Dealing damage with it will heal you + feed your heal resource meter, same like her Primary.
Her ult is a very long range beam that does pretty high damage + heals a massive amount of health to every friendly caught in the vicinity of the beam, and it requires Zarya-like beam tracking, although a bit more generous as it's a slight AOE around the beam. It ignores shields, and recharges your primary heals very quickly.
She seems like a great, deep hero that won't be easy to play, but a hero that can be very strong in capable hands. She requires a LOT of cooldown and resource management, and spamming heals isn't an option due to the limited resource meter and how slowly it charges without doing damage. Most of her damage goes through barriers, so I suspect she'll be great in breaking cheese and other shield-heavy comps such as Bastorisa/Torbisa and so on. At the very least she can feed some easy ult and heal charge off of them, and her ult is a strong damage dealer