Switching from a smartphone to a dumbphone is usually not about increasing privacy in the first place.
People tend to make the switch for mental health reasons, rather than privacy ones. When your phone goes back to being a direct communication tool rather than a passtime, you tend to realize just how much time you spend during a day doing basically nothing.
This is probably fine. The connection to DDG will be over HTTPS, so a captured packet would need to be decoded first. And if someone were to manage to break the encryption, then they would also need to know what service you used the password for.
Ultimately, it’s more secure to generate locally, but it would be a huge amount of work to get anything usable out of a packet capture