How bad does your 12 volt batt have to be to effect your ABS/VSC/brakes?

What directly matters isn't the condition of the battery, but what voltage arrives at the braking components. The system measures that, and will set code C1241 to let you know if ever:

• The voltage there falls below 8.9 volts for 3 seconds or more while you aren't braking, or
• The system can't supply enough current to one of the linear solenoids, while you are braking, or
• The skid ECU doesn't have at least 8.5 volts coming in (independently of the ABS NO. 1 or 2 relay), or
• The skid ECU's internal regulator supplying the computer logic goes out of range for a twentieth of a second or more.

The internal regulator's job is to take whatever voltage comes in (which can range pretty widely, from below 9 volts as you see to nearly 15 when the car is ready) and produce a steady 5 volts for the computer circuits to rely on. Such regulators can normally do their job as long as they've got a couple volts of headroom to work with, say, more than 7 coming in. The 5 volt regulator output is critical; you'll get a code if it goes below 4.7 or above 5.3 for even a twentieth of a second.

If you get one of those codes, it makes sense to check the condition of the battery, but if you don't find the problem there, it could be in any of the circuit path bringing the power from there to the brake components.

 

"How far can a horse run with a broken leg?"

Most points have been covered in the post above.

Where you might first see problems with a weak 12V battery is when you turn on the car. All power is initially supplied by the 12V, until the HV system comes online and the DC-DC converter takes over.

For 1-2 seconds the car draws 25amps or so from the 12V. (That's a tiny amount compared to the 150-200 amps for a typical starter motor.) If the 12V gets weak enough, voltage to any ecu can go below threshold during powerup and set codes.

Short form, have the battery properly charged and tested- if it fails then replace it.

There might be other faults that can cause brake system concerns, but first "establish a baseline" by verifying 12V battery condition.

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Yes, probably.
~12 V is not a valid measurement.
12.0 with no load is half discharged and potentially a problem.

You can't measure the actual battery voltage while the car is running (ready) because what you will see is the charging voltage.

 

ABS/VSC/brake lights will light if the ECU controlling them has trouble codes to report.

That ECU monitors the voltages arriving there (which are the ones that matter for this purpose), and it will set a C1241 code if the voltages fell short, at any time, of the limits shown in post #2,

The skid ECU can also report many other codes, for issues unrelated to voltage. Those will also turn the same lights on.

So if you have ABS/VSC/brake warning lights on and you want to know why, an important step is to find out what the codes are.

If you do not have a scan tool to use for that, you can retrieve those codes without any scan tool, using the method described here:

Blink (a/k/a Flash) Codes – How to. | PriusChat

That page mentions that the C1241 code for electrical supply out of spec corresponds to blink code 41. If that's among the codes you retrieve, then the electrical supply is a contributing factor.

 

At minimum the battery should be fully charged and properly tested (at a shop or store with proper equipment).

A good battery shouldn't really even go below 12.0V, - it should be 12.6 to 12.8 fully charged, and 30A for a couple seconds won't do much of nothing to that. If you go into the 10's, your battery is way discharged or just failed.

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... and still won't, at that point, cause you ABS/VSC/brake warning lights.

But as you can see from post #2, if it dips a little further than that, the voltage monitoring in the brake system will catch it, set the C1241 code, and show warning lights.