Hi mdrabble. I wouldn't want to insist on this as I may be proven wrong, but I've had to do a lot of Forms/Power Automate combinations this year and I'm pretty certain you can't do this... at least not with the standard getup of Forms. The power automations are triggered at the point a submission is made so it can only ever take action after the fact, not during (i.e. tell them on screen that it's rejected and not create a submission)
I can't test this myself right now so this may not work depending on what options Power Automate/Flow offers, but one idea in my head would be:
Form gets submitted
Flow/automate is triggered
Get all responses from said form
Conditional check if e-mail address already exists from any of them
If yes: send an e-mail to recipient that the submission was rejected, then delete said submission
If no: carry on!
That might be pure wishful thinking/easy to say on paper of course!
As a side, it might be worth investigating Microsoft 365 Dynamics - Customer Voice. This was formerly "Microsoft Forms Pro" and I've had a few occasions where a feature I would have wanted for our forms here is possible with that product. I don't know if this specific scenario would be covered (checking public responses for duplicates/e-mail field) but if I were in your shoes I'd certainly give it a look. It appears to be per-user licensing so the cost implication wouldn't be too bad I imagine, depending on how desperate they/you are to have this.
Hopefully this is of some help, apologies if not!