How do I stop messaging sounds from playing through Bluetooth speaker?

I play music from my iPhone 15 Pro (iOS 18.2) over Anker or JBL Bluetooth speakers. I do this most often to play brown noise when sleeping or working although sometimes it’s to listen to music in a social setting. Whenever I get a text, or call for that matter, the receiving and sending sounds play startlingly loudly through the speaker. I don’t want/need these notifications being broadcast for all to hear yet the only way I’ve found to stop this is to silence my phone, which I don’t want to do. I simply want these notifications to play through my phone, not the speaker. I’ve scoured my settings and the internet but cannot find a solution. Can anyone help me resolve this?