Although I am not fond of them the vertical blinds that cover our wall of windows and french door is completely private when closed. I've tried peeking thru them at night to look in my home and I can't see anything. the 2 step process of turning them before pulling them open however puts them on my less-than-favorite list, plus when closed they clatter if a vent blows on them. I had to buy vent things to blow the air horizontal not vertical. Also when the window is open and they are pulled open they clatter in the breeze and have to be tied back. they are tied back for this picture Here is a link that might be useful:

When you opened the door, the blinds would move, but it never bothered me. Before we moved in, the previous owners had hung mini-blinds, and there were hooks near the bottom to hold it in place. When we first moved in, I replaced the mini blinds with a roman shade, made by me. And I never used the hooks. When we renovated the kitchen 10 years later, we ended up replacing the door, and I didn't put hooks on the new door. This is when we put the faux wood blinds on. I don't think they swayed all that much because there was support behind them as it was moving. And we never swung the door hard enough to get a good force on the blind. And the trim around the glass sat proud a 1/4" or so, and the blind was slightly wider than the window, so the blinds never touched the glass. Thanks for the compliment on the BS. I had planned to just do white as we were already talking about moving. DH wanted orange. I came up with this "random" pattern to give him his orange without being solid orange. SIL is the only person who ever commented negatively on it, but it was enough to make me nervous when we put it on the market. But both realtors we interviewed also loved it. And the house sold in 2 days. So I guess it wasn't too crazy.

From what I can tell by the picture it looks like whatever you do will have to be an outside mount. The only thing I can see mounting directly on the doors would be 2 cellular shades. I would go with cordless shades. Now if you want to do something that will mount similar to verticals but aren't verticals, there are several choices. There pricing can vary widely! I will recommend that you read this blog article. It will give you a lot of ideas as to products available and an idea as to how they compare to each other price wise. https://dressthatwindow.com/i-hate-verticals-what-else-is-there-for-sliding-glass-doors/ Here is one idea, it is called a Vertiglide. One of the nice things about this product is that when you have it all the way open it only stacks 6 1/2" so it keeps your view. On that blog site there is also and article on drapery side panels if you want to do something and really give it a finished look! Good Luck!

Please post pictures of the area so we can see it to help advise you.