General specifications for that device show as:
Bluetooth Version 3.0
Bluetooth Support A2DP V1.3, AVRCP V1.5, HFP V1.6, HSP V1.2
I'd assume that if you have any Bluetooth, it is compatible with 3.0 because the newer one, LE is 4.0 and is usually backwards compatible with former versions. A2DP, AVRCP, HFP, and HSP are audio, hands free, and headset profiles and they are also pretty typical. Therefore it really depends on your computer and the software as to whether or not it can deal with the fact that an audio device is hooked up via Bluetooth. Do you have like a smart device, being a tablet or a phone where you can attach to this speaker and use it from one of those? That will pretty much validate that your JBL device is working, and my assumption is that it does work. Next I'd consider checking different things like a live boot of a different Linux or Windows and see if you can control the speaker from that computer, just with different OS or different software. But really, once you attach to the speaker, audio should be capable of playing through it. To debug it on Manjaro I'd say you should examine your system log looking for the discovery and attachment of the device and then check logs for the system and audio players for when you try to channel sound through it and see if there are errors.
By the way, what happens now when you try to play sounds? Do they just go through your system's wired speakers?