A few turns of wire around a screw would short out a battery like this. What's happening is that the Li-po is shutting off using its internal protection circuit.
Let's compare the two batteries when we connect a nearly dead-short load, like your 'few turns':
- AA battery: battery internal resistance limits the current, energizes the magnet
- Li-po battery: protection circuit detects a short, cuts off the battery, magnet does not energize
Non-energized electro magnet will still attract magnets, but won’t repel them.
Why does the Li-po have a protection circuit? Li-po and Li-ion batteries have very low internal resistance. Without protection, when shorted they will heat up very quickly and even catch fire.
Fortunately for you the protection circuit did its job, and you only had a non-functional magnet vs. a fiery YouTube-worthy disaster.
In future, never connect a dead short across Li-po or Li-ion battery. Add a series resistance to limit the current.
Related: Why is there so much fear surrounding LiPo batteries?
it only attracts other magnets
... remove power ... it will still attract magnets \$\endgroup\$