I had a chance to test her out in the PTR last night. She's pretty fun to play, but she's kind of underpowered. Her rifle doesn't deal much damage and it doesn't heal much either. She seems more of a mid range fighter like Hanzo than a truly long range sniper like Widowmaker. Ana's grenade is pretty good. It heals allies and increases other healing sources as well as damaging enemies and temporarily preventing them from healing. Her tranquilizer is also pretty useful, giving Ana a chance to escape a pursuer or make an enemy vulnerable to attacks. Her ultimate is pretty great. It buffs one of your allies, increasing their movement speed, damage, and making them harder to kill. Put it on a tank and they're sure to destroy the enemy team.
Overall, I think she's a good addition, but feels a bit weak. Especially now that Zenyatta is going to be buffed, he'll fill the role of a long range healer better than Ana.
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I think a support sniper is an interesting design. Can't wait to see her in action. I'm a bit surprised they introduced a character with such a direct connection to another character, though.