Its true.

A wallet is transaction signing software

Don't @me with "cloud software" like this is "cloud gaming" or some nonsense. Your "custodial wallet" is a bank. You installed a banking app on your phone.

nostr:nevent1qqs2we5gaz5hvfs382gz3wk70sxktcpk8a5rldus28u2356a25q5reqpp4mhxue69uhkummn9ekx7mqpzamhxue69uhkummnw3ezuendwsh8w6t69e3xj7spz3mhxue69uhkummnw3ezummcw3ezuer9wcq3kamnwvaz7tmwdaehgu3wwdmkjumn94jku6t8d4sjucmgqy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqgkwaehxw309aex2mrp0yhxummnw3ezucnpdejqz8thwden5te0wfjkccte9ehx7um5wgh8w6tjv4jxuet59e48qqgkwaehxw309aex2mrp0yh8qunfd4skctnwv46qzpc9p2