I think there's a setting for this. I don't have speakers to test it with though. Try adjusting the Audio Route setting in Control Center and the Audio settings in the VoiceOver settings.

I think what you’re describing would be controlled by the device sending the information (phone/computer) rather than the Bluetooth speaker. The technology within a Bluetooth speaker is actually quite minimal - it just plays whatever it is told to by the device sending the information. I don’t think the Bluetooth connection could be clever enough to filter out certain information because it would have no way of differentiating the information. It literally works like an amplifier - I’ll do whatever the phone/computer does but louder. So you would need to configure the phone/computer/app to not send VO via Bluetooth.

Step 1. Connect any Bluetooth speaker to your computer.
Step 2. If you’re pairing a second set of speakers or you would like voiceover coming through another audio device connect it to your computer as well. Playing voiceover through your laptopspeakers is an option.
Step 3. Head over to voice over preferences, and route your sounds setting to which ever sound source you would like voiceover to play through.
Step 4. Head over to your menu bar under the first stack of things to do in the section called Apple hip preferences, then head over to sounds.
In the sounds window, select outputs.
Step 5. Interact with the table in that window and select which source you want main audio to play through.
Edit 1. Line spacing.
Edit 2. Forgot to add the first edit.

I have a great sound card in my PC, and I route most of my sound with it. For my screen reader I have a USB sound card, that only plays to a set of headphones. This can also be done with certain app specific settings. Just how I do it.

The speaker has nothing to do with that. There's an audio destination thing you should be able to add to your rotor if I'm not mistaken. It'll let you choose where VO's audio goes. You'll probably have to do it each time you connect to the bluetooth speaker though.

Hi, I know what you mean. I have two bluetooth speakers that do different things. My JBL Charge only plays the music on the speaker and a cheep non-brand speaker sends the music and VO to the speaker. There is no setting to make this happen as far as I know.
My JBL used to send VO to the speaker, but one of the updates on IOS made it change.

VoiceOver does not speak through AirPlay speakers like the HomePod, however you won't be able to listen to audio from videos through them either.

AirPlay does not work through Bluetooth, but you can still play audio through it using an ad-hoc WiFi connection which is created for you automatically when you allow everyone's access to your speaker with an optional password.

I think if you connect Bluetooth headphones or speaker, a setting comes up on the rotor, where you can decide to play the sound from the speaker or phone.