Stop Alexa from playing music on Apple Watch SE

Re: "I don’t have Alexa app installed on my watch yet somehow music plays when I listen to a Bluetooth speaker or Echo Dot. I would like to disable this feature ... "

Seems Alexa may be set up as the default for the speaker ?

... perhaps you can turn that off in the same way it is turned on?

Eg: Play Apple Music with Alexa - Apple Support

says:

"Set up Apple Music as your default music service

If you don’t want to say “on Apple Music” every time you ask Alexa to play something, you can make Apple Music your default music service on Alexa. Here’s how.

1. Open the Amazon Alexa app.
2. In the bottom-right corner, tap More.
3. Tap Settings.
4. Scroll down and tap Music & Podcasts.
5. Tap Default Services.
6. Under Music, tap Apple Music."

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Resource: Apple Watch User Guide - Apple Support

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Else: If needed: You might want to reach out to the Apple Watch Support Team.

There is a "Get Support" link (scroll to the very bottom) on their webpage (link below)

Apple Watch - Official Apple Support