What's the most important check on a used EV?

Battery State of Health — ask for a diagnostic readout, not the range estimate. It's the single biggest factor in value and reliability.

Does the battery warranty transfer to me?

Usually yes, but confirm it and how much term remains — manufacturer battery warranties are often 8 years.

Get a battery State of Health (SoH) readout — a diagnostic figure, not just the dashboard range estimate. Below ~85% on a relatively young car is worth questioning.
Ask about charging history — constant DC fast-charging and habitual 100% charges age a pack faster than gentle home charging.
Confirm the manufacturer battery warranty transfers and how many years/km remain (BYD packs are commonly 8 years).
Check the tyres — EVs are heavy and torquey, so uneven or fast wear is common and tells you how it was driven.
Check the brakes — regen means friction brakes are lightly used; look for caliper seizing or corrosion from underuse.
Verify the Certificate of Registration details (owner, motor kW) and that all import/Customs papers exist.

If the seller can't produce a SoH reading or the battery-warranty status, treat that as a price risk — the battery is most of the car's value.