tolkiens legendarium - Did Saruman continue to exist as an ethereal Maiar after he was murdered?

Inspired by What was Saruman the White's purpose?

The Istari are Maiar in corporeal form - it seems evident that some aspect of the Istari continues after the death of their corporeal (and can even reform as flesh in the case of Gandalf).

Is there any canon or notes from Tolkien to indicate that Saruman returned to the ranks of the Maiar as a non-corporeal?

Answer

TL;DR: Yes, he continued to exist as an ethereal Maiar after he was murdered, but he was without any power and he was doomed to wander but never to return to Middle-Earth

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Well, he didn't actually die (since he was a Maiar, like you said), but his spirit separated from his body much like Sauron's after the Downfall of Númenor. As an incorporeal spirit, he should have been called to the Halls of Mandos, but the tale implies that he was barred from returning. Tolkien indicated that his spirit was left naked, powerless and wandering, never to return to Middle-earth:

Tolkien says:

"Whereas Curunir was cast down, and utterly humbled, and perished at last by the hand of an oppressed slave; and his spirit went whither-soever it was doomed to go, and to Middle-earth, whether naked or embodied, came never back"

I found an interesting discussion here.

Also, from Return of the King:

…about the body of Saruman a grey mist gathered, and rising slowly to a great height like smoke from a fire, as a pale shrouded figure it loomed over the Hill. For a moment it wavered, looking to the West; but out of the West came a cold wind, and it bent away, and with a cold sigh dissolved into nothing […] long years of death were suddenly revealed in [the body], and it shrank, and the shriveled face became rags of skin upon a hideous skull.

That was more about what happened the moment he died. (When Tolkien refers metaphorically to the grey mist appearing like a pale shrouded figure gazing almost imploringly to the West), it is plain that a great wind, like the pounding of a judge's gavel, passed final judgement on both of them and dispersed their spirits forever. Unlike Morgoth, whose spiritual and/or physical manifestation was imprisoned until the final battle at the end of all things, Sauron and Saruman would remain incorporeal and impotent, and would no longer plague Middle-earth.