I played a few hours of competitive on the PTR to get a better feel of Ana...not 4 of her per team like QP is right now.
This is my opinion as a ranked 40 player, with just a few hours with her.
As a sniper for damage...she's simply horrible in my opinion. Her body shot does little damage, has no headshot bonus, and has a very slow firing rate, and only 6 charges. Her lack of movement ability to get to the good sniping spot means that every single class can get to her...which pretty much sucks for a sniper. She doesn't have an alternate firing mode like Widowmaker for when in close range...she can be in scope mode or non scope mode, but damage is the same, firing rate is the same, etc..
As a sniper healer, that's actually tons of fun, but suffers from the same issue as when dealing damage...cannot reach good sniping spot, slow firing rate, and kinda low heal...it's not as bad as her damage feels, but it's not great either. The other issue is when healing from a distance...your teammate are constantly out of line of sight.
So for her basic gameplay, I found her to actually work a lot better in mid-range and not using the scope, and just firing normally. You can target for healing just as easily and can deal damage just as easily...you have a lot less issue with line of sight making it significantly easier to heal. This also allows you to benefit from your grenade heals.
So that part of her is very underwhelming in my opinion...even though it tons of fun to play her.
The stun dart, it's a great as an interrupt...can be a great mez but will most likely be extremely hard to use as such since coordination for the group to not hit the sleeping person will be very difficult. It's great a great escape tool though if you don't miss.
The grenade...it heals for a significant amount, increase healing received for 5-6 seconds, it also damages enemies, and prevents healing for 5-6 seconds. It has a fairly small radius, but can be thrown very far. It can be extremely powerful and turn the tide of battle in a confined area where you can hit 2-3 allies and/or 2-3 enemies.
Now for the ultimate, it's simply crazy powerful in my opinion and I doubt it will go live as it is...it boost damage, increase damage reduction, and gives a speed boost. It very often ends up with a team wipe when used...withoit even requiring the affected player to use their own ultimate. I've seen a few Rein and Winston wipe the other when boosted with it.
Overall, she feels underwhelming in regular gameplay, low damage, somewhat low healing, and no mobility to speak off make her feel a bit weak...that is offset by her grenade and ultimate which to me feels very powerful. My issue is that she doesn't work very well as a sniper. She will be at best very situational. I think Mercy will still dominate as a healer, followed by Lucio...and quite possibly by Zanyeta now who is a serious threat.
My favourite map so far with her, and I haven't played her everywhere was The Temple in Nepal. It was easy to get a good range position, and heal from afar, throw grenades in the small control point always hitting a few allies and enemies. It's probably the map where she felt the most like a sniper healer and played like she was designed to.
Looking forward to her on live.
And damn do I love the no hero stacking in competitive.