Does mahayana believe in omniscience of the Buddha?
In Mahayana omniscience refers to prajna-paramita, the perfection of wisdom also known as the knowledge of all modes.

This comes from direct realization of Emptiness, and results in Buddha having no position, not leaning on any dharma or sign. Not assuming anything as the absolute point of reference. (There are many ways to talk about this.)

Having no position, Buddha knows all positions and all modes of cognition. Hence, the knowledge of all modes aka omniscience in short.