Hegel's system is essentially a continuation of Spinoza's system, with a teleological twist. In Hegel's system, there are tensions that are resolved and subject's evolving to an ultimate purpose. In Hegel's system subjects positively advance throughout history, in order to achieve some telos, the realisation of Spirit. Hegel accomplishes this by encouraging communitarianism and improving the society's arrangement (i.e. to achieve the nation's spirit).
It is incompatible with Vedanta because there, historical evolution by such progress is considered negative affirmation with the material world (the illusion). Brahman is already a perfect ultimate reality, and by our profuse karmic actions, we are fostering the larger dualism, we spur the clinging to our bodies, passions and goals, thus dissociating from the One. The cure is detachment from these:
One who performs his duty without attachment, surrendering the results
unto the Supreme Lord, is unaffected by sinful action, as the lotus is
untouched by muddy water.
— Bhagavad Gita
One who sees inaction in action, and action in inaction, is
intelligent among men.
― Bhagavad Gita
Hindu sages are frequently ascetics who deprive themselves of food or other life pleasures in order to release themselves from the illusion of changing world (Maya) and reunite with the whole. Through meditative absorption that extinguishes the attachment, they become one again and embrace Moksha- the liberation from the illusion (also the illusion of history).
When a man dwells on the pleasure of sense, attraction for them arises
in him. From attraction arises desire, the lust of possession, and
this leads to passion, to anger.
From passion comes confusion of mind, then loss of remembrance, the
forgetting of duty. From this loss comes the ruin of reason, and the
ruin of reason leads man to destruction.
― Bhagavad Gita
Hegel's system does not have any such negative concept of karma, action, or duality, and doesn't consider the world an illusion (because history is a real manifestation of Spirit). Rather, it embraces material affirmation, progress and changes. It goes through history to achieve the restructuring of human's society via ongoing positive process of perfection, in order to best represent Spirit.
With Hegel off the table, the direct inspiration and influence in Western philosophy would be Schopenhauer's idealism since he based his philosophy on large portions of Advaita Vedanta (and Yogacara).
In Schopenhauer's monist system, the Will (thing-in-itself) is akin to Brahman, and the liberation is achieved similarly; through either antinatalism, to reduce the suffering, or inaction through meditative absorption, i.e. immersive contact with the beauty. This is akin to Moksha, and Schopenhauer also explicitly embraces the Eastern notion of non-duality.