Short answer. An eBike battery is safe if it has a UL 2849 or UL 2271 certification, shows no swelling, cracks, or burn marks, does not get hot during charging, and comes from a reputable brand. Uncertified or damaged batteries are a fire risk.
Step by step
Look for UL certification. UL 2849 covers the whole electrical system, UL 2271 covers the battery. Both are printed on the battery label or in the owner manual.
Inspect for physical damage. Any swelling, cracks, burn marks, dents, or leaking fluid is a stop riding immediately warning.
Check charge temperature. A safe battery gets warm during charging, not hot. Hot to the touch means the BMS is failing or a cell is going.
Get an inspection if unsure. Mobile battery safety inspections take 20 minutes and give you a written pass or replace recommendation.