Alexa devices aren’t great for privacy, but they’re not nearly as bad as people like to think. They’re surely not as bad as your phone, especially if you’re not installing a bunch of skills.
They don’t send any data out unless they’re activated with the wake word. Alternatively, that means everything you say after that wake word is being recorded and sent to Amazon and who knows who else after that. By far the biggest privacy concern with them is when they mistakenly hear the wake word, and start sending data out without you realizing it. If this is a concern to you, I’d suggest leaving it unplugged when you don’t plan on using it, or plugging it into a “smart outlet”. Get a reputable one because that brings its own set of security and privacy concerns, or get one of the RF ones that turn on/off with a remote.
You can use Wireshark to sniff the packets leaving your network. I use a PiHole to see all of my network traffic.