Toyota NO Warranty

IMHO, you should go to another dealership. Your currently covered by Toyota's 3 year, 36K mile bumper to bumper warranty - unless your car has a 'branded title'. You can wait and make the complaint on your next free service interval - 2 year, 25K mile free maintenance. Get the problem documented, so you have proof that the issue was occurring during the warranty period.
If something is in deed pulling a constant 3.4A with the car off - That is not normal and Toyota is on the hook for the repair - unless it's some aftermarket item that you had installed. Something as simple as one of those insurance company OBD dongle could be causing the excessive draw. The dealership would be well within their rights to charge you a diagnostic fee for that.....

Good Luck.....

PS. You know there's a stealth battery recall on some of those cars. The factory received a bad batch of batteries. Tell the service advisor to look up the TSB on that issue.

 

This doesn't help,,, but know that every time a lead acid battery gets that low, it is a giant step to End of Life.
You have a much older, closer to death, battery now.

 

there are many threads here on the gen 5 12 volt draining problem.
i suggest reading through them so you can educate the dealer service manager.

 

If it has been acting like you described it, it has sulfation and needs to be replaced.

If you don't mind spending about $140, I recommend replacing it with the Uplus EN LN1/DIN H4/BCI 140R AGM battery sold at Amazon, which solves the battery-degradation issues resulting from infrequent charging by the Gen 4/Gen 5 battery-sensor-equipped battery-management system.

AGM battery for Gen 4/Gen 5 Prius/Prius Prime and observations on the 12-V charging system | PriusChat