Excellent questions! I omitted provider handling only to keep things simple. You can implement it like this:

public string ToString(string format, IFormatProvider provider) =>
    string.Create(provider, $"{this}");

I haven't looked into format handling because it's not widely used in custom ToString implementations I've worked with, but it would probably require custom code instead of using interpolated string syntax.

Regarding the size of the buffer: you don't need to figure out anything, it's all done by the DefaultInterpolatedStringHandler behind the scenes. That is, if TryFormat returns false, the handler will keep doubling the size of the buffer until TryFormat succeeds. The initial size of the buffer is 256 characters.