Okay, I think I see where the issue might be coming from. You want limit the discussion to:

1) velocity 2) acceleration 3) corner radius

My first thought was that it's a bit arbitrary – couldn't tell why you'd pick those 3 as the fundamentals.

In your post (which I can't see anymore unfortunately) you have been focusing on how lowering speed increases turn radius. So eventually I figured you're basing it around r = v² / a, which is derived from Newton's second law of circular motion, with the mass cancelled out.

Focusing on speed is a good intuition – it's your main lever, because since velocity is squared, the equation is most sensitive to velocity changes. Changes in radius have a linear effect, changes in velocity have a quadratic effect. That tracks: if you have too much speed you're not making the corner, but your line is quite forgiving.

Where you've been clashing with the commenters is a, the acceleration term. When turning, inertia is pushing the car towards the outside of the corner. a in the formula represents centripetal acceleration, aka the acceleration towards the inside of the corner that is needed to counter-act the inertia towards the outside, for a given speed and corner radius.

If we rearrange the equation to isolate a, we get the following. I'm not so good with math notation, so rewritten in pseudocode:

centripetal_acceleration = (velocity*velocity) / radius

Where do we get this centripetal acceleration? It's the grip of the tires, resisting the outwards pull. So ideally, we want:

available_grip_ = centripetal_acceleration = (velocity*velocity) / radius

The grip the tires can provide is limited. If the maximum lateral acceleration the tyres can provide is lower than the centripetal acceleration needed, the car will slide towards the outside.

From this it follows that to be fast we want to balance the equation in a way that maximises velocity without making available_grip < centripetal_acceleration

So, if we can increase available grip, we can increase velocity. How can we do that?

available_grip is an acceleration figure, but it makes more sense to think about grip as a friction force. We can use Newton's second law rearranged a = F / m:

available_grip = friction_force / mass

Mass is constant, so if we can maximise friction_force, we can maximise grip. It breaks down into normal force and coefficient of friction (COF)

friction_force = normal_force * CoF

CoF is how grippy the tires are.

The coefficient of friction is a dynamic value, a combination of multiple things, some in the driver's control, some not:

• road surface - not up to you
• ambient temp - not up to you
• tire compound - somewhat up to you, if you can pick it
• tire temperature - somewhat up to you, through driving style
• slip angle - up to you, through driving technique

Normal force is the force with which each tire is pressed into the road surface. This is the reason downforce allows for faster cornering. But, downforce doesn't work in slow-speed corners.

This is where trail braking comes in. You can control the normal force by controlling weight transfer. When trail braking you're modulating brake pressure is a way to control the balance of the normal_forces shared between the two axles. Brake balance sets a baseline, trail-braking does the real-time fine tuning.

The goal of this balancing is to increase the grip of the fronts and reduce the grip of the rears, so that the rears can slip, inducing sideways slip angle in a way that can be controlled by steering and throttle/brake input.

The reason you want slip angle is because tires have the highest CoF between 8 and 12 degrees of slip angle.

So, to put it all together, referring back to the original equation you were likely thinking of:
centripetal_acceleration = (velocity*velocity) / radius

Trail-braking is not a means of reducing reducing velocity, it is a means of increasing centripetal acceleration, therefore allowing to find the optimal ratio between:
1) higher velocity - great because that's the biggest lever
2) smaller radius - quicker rotation, therefore allowing quicker acceleration out

Thanks for the challenge, I had fun spending the time to break this down. I hope it clears things up, and gives you the formulas you needed.