I would build a wall around the chimney and then put a metal roof over the entire deck.

A Coolaroo shade sail : https://www.coolaroousa.com/category/outdoor-shade-privacy-shade-sails

A patio umbrella should work.

Paul, we have had a Sunesta(spelling?) retractable awning for over 20 years. We have replaced the material once since then...very pleased.

I'm thinking this is what she's decided on to best fit her needs.

If you get the cantilever ones, or whatever they;re called, you can set the pole at the railing and get more coverage over the deck, and those umbrellas are bigger...

Got a big ol' umbrella.

They come in a bunch of sizes. We spend a bunch of time in ours during the summer. I just store the canopy in the winter leaving the structure up.

https://www.menards.com/main/doors-.../p-3289655540241493-c-9001.htm?exp=false

Good choice for that situation.
You can add to the pole to make it higher for more creative options…. Like more shade.
I would figure out were you want the umbrellas to be and drill though the deck and put the support under the deck…
And add extras.
You can make caps to hide the holes

No more visible stands….

It goes through the middle of a table and rests in a heavy base.

Was just looking at umbrellas, I see they have a 6.5 and an 8' x10' rectangular one, pretty cool....still folds up like a regular umbrella and goes through the center of a table...buy needs a HEAVY base....

Some of the newer models of umbrellas are pretty cool. As mentioned above, they make cantilever models, straight poles, and tilt models. Most are very reasonable. A crank up and down model for the canopy is a must in most area, as wind is the enemy!
Glad she found what she is looking for.