Is the problem that the boards don't lap one another and aren't straight so there are gaps that show the studs and insulation in the walls?
From your picture, it looks good. I can't see anything in the gaps. Is it different in person?
I think chinking looks appropriate in real log cabins and timber framing. I think in your application it would be very tedious to apply it in every crack to achieve a look that was better than just leaving it alone.
I grew up in a 1920's house. The original interior walls were all sheeted with 1/4" redwood plywood. In some areas my dad used wood similar in size to yours on the walls, but pretty thin. It was like 3/8" thick stuff, all clear old growth back when you could get that stuff. There were areas where he took the plywood off, like where he rebuilt the brick chimney and where he made access cuts for wiring and plumbing.
You could always just barely discern where the plywood backing wasn't there because the minimal space between the boards looked a tiny bit different. You couldn't see anything in there, but if you stared at the wall it was noticeable.
Probably a good idea to use a thin wood or dark colored backer under wood paneling without a shiplap or tongue and groove to mitigate that issue.
In your shed, in the middle of nowhere, I think you've already gone way above and beyond and anyone would be impressed with your workmanship.