I haven't encountered any info indicating they don't self custody. Everything I find shows they hold their own keys.

https://cryptoslate.com/tesla-shifts-entire-765m-bitcoin-holdings-sparking-strategy-speculation/

https://crypto.news/elon-musk-misquotes-bitcoin-self-custody-mantra/

https://www.forbes.com/sites/digital-assets/2024/10/26/tesla-bitcoin-moves-may-no-longer-shake-the-market/

https://cointelegraph.com/news/tesla-buying-bitcoin-btc-wallet-curiosity