I have Jax unmatched on board, my enemy is targeting it with Stars Crossed, I play Shady Spectacles with quickdraw due to Jax effect on him and make him a copy of other unit. Does Stars Crossed still bounce him or is he a new target?

Yes, Star-Crossed still bounces Jax. The copy effect from Shady Spectacles doesn't break the targeting relationship.

Here's why: Targeting is established when Star-Crossed is finalized on the chain (Rule 355.14.b). Jax was a legal target at that point — he was an enemy unit on the board. When Shady Spectacles later resolves (via Quick-Draw's attach trigger) and makes Jax a copy of another unit, it changes his copyable traits (name, abilities, Might, etc.) but doesn't change his zone, his controller, or his status as an enemy unit. Per Rule 359.3.e.2, a target becomes illegal only if it no longer meets the spell's targeting requirements or changes to/from a non-board zone. Jax is still a unit on the board and still an enemy — he's a perfectly fine target for "return an enemy unit to hand."