What are the assumption of Gibbs free energy equation referring to the system and the surrounding?

The system for

$$\mathrm dG=\mathrm dH-T\,\mathrm dS$$

is a constant temperature and pressure throughout the process, only volume work is possible and it is in thermal equilibrium with the surrounding. Is that right? Are there any other constraints?

$$G \equiv H-TS \Rightarrow dG = dH - d(TS) = dH -TdS -SdT$$
Then, to get your equation, the only restriction we need to add is constant $$T$$:
$$dG= dH -TdS$$
Why, then, might you be associating this equation with the more extensive restrictions of constant $$T$$ and $$p$$, and no non-$$pV$$ work? I suspect it's because, to use $$dG = dH -TdS = 0$$ as a condition for equilibrium, these other restrictions are required. For more on this, see the end of my answer at What is wrong in this argument that dG must always be zero?