After using a syringe to remove and refill the reservoir, can you turn the car off, put on a brake pedal depressor and use the bleeder nut to drain the lines?
There is a "fluid replacement procedure" given in the repair manual that you can follow without needing a scan tool. Toyota Service Information and Where To Find It | PriusChat I think a bunch of existing threads here describe it. Best to follow that procedure. Keep in mind that a job is only "fluid replacement" if there is no air in the system to start with, and if you take total care the reservoir never gets too low and no air gets in while you're replacing. Otherwise, it becomes an "air bleeding" job, and there isn't a no-scantool procedure for that.
FWIW; hopefully you disconnected the battery before you sucked the brake fluid out of the reservoir. The system does periodic testing and if the brake test was triggered while it was empty; it would've sucked air into your brake system. This isn't an old simple hydraulic brake system; there's a pump and ecu atttached to it.
I’ve done a couple of non-Techstream brake fluid replacements; it’s a straightforward procedure, works. Some links, tips and repair manual excerpts in my signature. Worthy of note: the parking brake must be applied for the “invalid mode” to activate. (on a phone turn it landscape to see signatures)