Misunderstanding of output impedance and linearity
You have to separate some things first.

Thevenin by itself has nothing to do with output impedance. Thevenin is just a method for "shuffeling around" sources and impedances (resistors) and represent them in a different way which is sometimes convenient. For example:



This only whorks for linear elements and therefore only for linear circuits.

Output impedance is also only defined assuming that a circuit behaves in a linear way. We can however define for example output impedance of a non-linear circuit by linearizing it around a certain operating point.

This is what is for example done for all transistor based circuits which have a (somewhat) linear behavior for small signals but have a non linear behavior for large signals.

For that large signal behavior we cannot define an output impedance but for the small signal behavior we can. And in case that results in an inconvenient circuit, we could use Thevenin to represent it in a different way which is more convenient.