what exactly is thermo dymanic equilibrium? do the state variables remain constant w.r.t. to ohter systems or surroundings, or do they keep changing uniformly?

Thermal equilibrium means that there is no temperature gradient in the ‘system’. Now you can reason this out in the following way- If there is a temperature gradient, then you will have a non-zero thermal current in the system which definitely doesn’t describe thermal equilibrium. Besides, you can keep in mind that equilibrium is a state of minimum energy. Therefore, the system is at a temperature at which its enthalpy is minimum.

In mathematical terms, you can say  dH/dT =0.