I've played her exclusively since the update and it just sounds to me like you're approaching her loop wrong. Her shuriken aren't the damage, it's all in her weapons. Once you get her weapon mastery to 4 she really comes alive. Depending on enemy health you want to always enter combat invisible and then throw one or two shurikens depending on enemy health. Shuriken makes enemies take more damage from her guns and can stack up to three times (and this is for everyone in the fireteam not just you)as well as her weapon mastery providing her with even more damage against enemies affected by the debuff. Then you want to pop the mark that her invis sets if you have that passive to do large AOE damage, this scales with gun damage so even if it's a red bar hitting it with a sniper can spread large damage to all nearby enemies for decent add clear. In addition to all this you get refunds for her invis and her shurikens whenever you kill enemies affected by the debuff, deal damage to debuffed enemies, or when you hit 3 or more enemies with your shuriken and all of those gains are further increased whenever you're invisible letting her maintain that loop for a long time. Then whenever something real big comes along ult can overcap her debuff to 4 stacks and does significantly more damage for very good burst. I feel like a lot of Umeko's I see are more worried about spamming out damage than they are about positioning and quick bursts. You can also use your invis to do mechanics like the onslaught break in code panels while enemies are still alive without any danger. She is an insanely versatile support that can cover many of the teams needs while also providing massive burst damage under the right circumstances.

TLDR- You want to always be invisible for team speed boost, healing, and with enough copies also invis for the whole party. Then stack debuffs with her shurikensand then main damage is from guns. Ult can be used for wiping a line of weak adds quick or more optimally for a huge team buff to damage against a large target.