Is it possible to connect LiPo level indicators in parallel?
Easy: That is a definite NO

Your LiPo cells are in series. The orange and purple connections in your second drawing are the same as the connections directly above them where you switch the LiPos in series.

So there is a straight path: from purple wire down, purple wire up to the right, up to the battery contact hopping over to the battery where we started from. That's a DEAD SHORT.

You might have drawn the connections above and below the battery as separate connections but they're not.

I have drawn two of these shorting paths.



It will ruin your day ! So don't !