A clever little puzzler that leverages the burglary theme really well with the swap-with-anything mechanic.
Though the abilities were cool and well implemented, I found very little use cases for the lane-shift (though in retrospect, it would have been handy for moving security cameras), and the invisibility was too overpowered, being an actual get out of jail free card.
That's not to say these should be removed, least of all the lane shift, but rather I suggest things become more difficult at a faster pace so that those abilities become more valuable and integral to success.
Expanding on a suggestion from another commenter, to use predetermination in the enemy spawns in place of randomness, I put forth: why not both?
Have each enemy randomly spawn on the map, but at predetermined intervals.
Add a security guard every level, riot guard every third, and a camera every fifth, for example.
Another possibility as the levels get bigger (at the risk of feature creeping) is multi-tile tetris-shaped furniture that cannot be be swapped with. Perhaps even single-tile objects that can be swapped that block the view range of cameras, such as a potted plant.
You're off to a great start with this one. Keep up the good work! :D