Can you do split panels so they stack on both sides like drapes would?

Can you hang a single stationary panel on the left so it will appear symmetrical with what's going on on the right?

I probably should've mentioned that we prefer the stack on the right since we let the dogs out the patio door at night and it's easier to open the panels just a crack and open the door. If we do a split, then we'd have to open it all the way to get access to the door.

Hanging a panel on the left..didn't consider that but it would be a custom thing.

Looking at them on the website, it looks like the smallest size you can get is 36", so part of the window will be covered up no matter where you mount it. You could probably put them slightly off center, but too much or it would be noticeable.
I guess it depends on if you could live with that or not.
Perhaps you need to consider another window treatment that stacks better, would be centered and clears the glass.

I dont blame you for not wanting to block the view but then yes, since sliders are centered on wall it will no longer be if bar extends only on one side so blinds can be pulled off window.

What a bout a curtain rod thats centered while also extending beyond the left/ right of window so curtains opened will be in front of wall, not blocking view.

We replaced our vertical blinds with curtains after seeing it on a neighbors sliders - got panels with built in top rings so easy to slide them open / closed.

Dining rooms dont have a lot of options for fabric to warm up the room like bedrooms/ living rooms have. Liked how curtains soften the feel of dining room too. Plus my own quirk but when I see vertical blinds, cant help but think they give look of being in an apartment. Lived in plenty of them so not being snobby, just not a fan of it.

On them, we