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)
you need to put the car into invalid mode to bleed the rear brakes since it’s controlled electronically. The fronts you can bleed the brakes conventionally by having the car off and pumping the brake pedal and hold and opening the bleeder valve.
When there's no air in the system (you just want to do "fluid replacement") that works ok. "Bleeding" (which traditionally means "getting air out") is more complicated: the actuator has multiple fluid pathways (for normal use and for fail-safe use), with electronically-operated valves between them, controlled by an ECU. Attempts to do what you'd do to bleed your grandpa's brakes don't get the air out of all the places, except when you're using the scan-tool bleed procedure that operates the valves at the right times.
I recently tested the brake fluid on my 14 year old 2012 Prius v. I used both the Phoenix dip strips and the moisture test light. The strip show no degradation and the light showed no moisture. I was going to have my dealer bleed and change the fluid, but now found that it isn't necessary.