This is what our lawyer told me:
"The Travel Rule applies when one of the parties involved in the transaction is a CASP (Crypto Asset Service Provider) and for transactions exceeding €1,000. It does not apply to transactions between self-custodial wallets (i.e., when a user sends funds from their own non-custodial wallet to another non-custodial wallet)."
"The Travel Rule applies when one of the parties involved in the transaction is a CASP (Crypto Asset Service Provider) and for transactions exceeding €1,000. It does not apply to transactions between self-custodial wallets (i.e., when a user sends funds from their own non-custodial wallet to another non-custodial wallet)."