Catch them early evening or a weekend afternoon when things are calm not right after a loud spell but then try, “Hey, I’m in 3B - sorry to bug you. I’m up at 6 for work, so if you could keep music low after 10, I’d appreciate it,” and offer to swap numbers for a quick text if it ever gets loud. If it keeps happening & use a fan or white noise, move your bed off the shared wall, and keep a simple noise log you can share with the landlord only if needed.
Good call on the gentle precharge. Before you go there rule out simple stuff: try a known-good pack to confirm the charger is fine, and make sure the small center/sense pin on the battery isn't dirty or pushed in since a bad thermistor contact will also cause a blink fault. If it's Li-ion and it sat deeply discharged, it may come back with reduced capacity; stop and recycle it if it heats up or swells during charge.