Word request for the action of throwing the sheets over a bed

A single verb can describe sequential actions whose individual descriptions are usually unnecessary in common speech, but might be employed in vivid storytelling or a work of highly mimetic fiction, especially when the sequence is interrupted.

For instance, opening a door requires an approach, reaching for the knob/handle/whatever, activating this device, stepping back while holding the knob, etc.

If something interrupts the sequence, one might say

I had just begun to open the door when …

Or in a more vivid narrative

My fingers had barely grazed the door handle when …

Spreading a sheet on a bed or a towel on the sand is a similarly sequenced action where the airborne portion usually doesn't need to be described, mainly because except in the narrative situations I mentioned, it simply isn’t topical. Thus the blank stares.

So what about vivid narrative?

The isolated action is similar to what you do after lying on the beach towel until sunburned: you shake out the towel to get rid of the sand, or if you couldn’t resist eating crumbly cookies/biscuits in bed, you’d shake out the top sheet to get rid of the results. You perform the same action on a rug held out the window or to fluff out a towel you’ve dried on a clothesline, though in these contexts, the action is usually repeated a few times. It’s a kind of whipping motion you would rarely have to describe further.

Spread is the most suitable word.

The Ngram Viewer doesn't find anything for unfurl or unfold a blanket, but it has many hits for spread a blanket.

By the way, the word bedspread is synonymous to blanket, which shows the suitability of the verb "spread" to talk about spreading a blanket.