Basically, I have completed all the mission quests,
I have the flash drive, and I've got out of the underground,
but for some reason the game did not mark 'find the way out' quest as accomplished,
and thus the entire mission is still active in the PDA,
even though I found the stash, took the stuff, and left the area.

Since then, I finished the work in Dark Alley and X-18,
got through the Wild Territory,
and now I'm in Yantar on my way to X-16.
The 'Strelok stash' mission, however, did not disappear.

I wonder if there is any way to fix this?
Since this mission is part of the main story line,
I wonder if it has any effect on the gameplay,
if I leave it as it is?
I would hate to go all the way back to Agroprom again.

You got out of the underground, but not the way the devs wanted you to go, which involves a lot more fighting.

I don't think you will have any real problem finishing the game. The mission is not part of the "main story line", it is part of your story line.

The only effect it has on gameplay is an annoying unfinished task in the PDA.

You can fix it with ZRP if it bothers you that much. ZRP works with vanilla saves, so you don't lose any progress you have already made, although it does have a feature to create a save at the approximate point of progress in your game if you need to.

To complete the task, install ZRP and load your last save. That's it.

Edit: ZRP = Zone Reclamation Project, a bug-fix mod for STALKER SoC