This is a super solid start to a great puzzle game, and it's executed very cleanly here.
You say this is your first jam game, so you should be so proud of yourself for scoping responsibly, and btw huge props for actually coming up with a bespoke puzzle mechanic within the jam window (that's not easy)!
If this was ever to be extended with some new mechanics, I would absolutely play it. The jam version has issues with a simple dominant strategy* working for every puzzle, but that can be corrected with some meaningful new mechanics that complicate things.
Congratulations on the submission! I hope you keep making games :)
*No paths need to be evaluated by the player. They simply need to find the 1 tile no other tiles point at, and that tile is the correct first-click every time (this can be done surprisingly quickly). Because of this, the 4-way and "jump" tiles aren't meaningful mechanical additions because they in no way change the player's approach to solving the puzzles.
Some other players have noticed they can brute-force the puzzles by clicking randomly, observing which tiles weren't activated, and narrowing down from there, but this is actually enormously slow in comparison, so it's a lesser concern (and can be addressed easily later with some minor design tweaks.)