NOT logical. Tested.
Read below.

I set the following challenge:
Create a puzzle where the numbers on the left are palindromic, the numbers at the top are symmetrical, the puzzle is logical... and the puzzle itself is not symmetrical.

Challenge set in the comments section here:
https://www.hanjie-star.com/picross/lamp-25123.html

Robaharrison attempted to take me up on the challenge, and did a great job, but didn't quite manage it:
https://www.hanjie-star.com/picross/challenge-from-baggy-t-18483.html

This is a puzzle that satisfies the conditions for the numbers (top numbers symmetrical, side numbers palindromic), but it is not logical.
In fact, there are 2 solutions: the one that works, and the mirror image.

Therefore, I have to tell you that the very top left square is filled. Now it can be completed.

Part 2 coming soon, with an explanation of a piece of logic for such puzzles!