Hi Philippe,yesterday I tried what I had in mind, but testing the various combinations it only partly solved the problem in Debian 13, and even less in testing/unstable. So I did more tests and made a different change, which seems to work around the problem in the various cases: cinnamon will recommends libspa-0.2-bluetooth (the PipeWire Bluetooth plugin) directly.
Unfortunately, from what you describe (the headphones pair, but then the connection is refused with "br-connection-refused", even with the PipeWire Bluetooth plugin installed), you may be hitting a different bug, which can't be solved by simply installing a package. I don't have Bluetooth headphones to reproduce the problem and debug it, so guiding you through the debugging could be complicated or long.
Another bug came to mind, and I don't know whether it could be related: https://bugs.debian.org/1126547 (an assertion failure in cinnamon-desktop's volume control library when a Bluetooth headset connects with PipeWire). It's fixed upstream, but even if it looks relevant, the changes are significant, so I'd rather wait for Cinnamon 6.8 than spend a lot of time backporting and adapting that and other commits, and testing them, not to mention that I don't have the devices needed for complete manual tests.
Regards, Fabio
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