In the international rules, it's rule 41 outside help.
It is not specific to radios, although many regattas specify that in the Sailing Instructions.  Your national prescriptions and some class rules may also further restrict what you can do with transmissions.  If you are using this headset for team racing, between boats on a team.  That also could be problematic. 
Ordinarily if the signal starts and ends in the boat you are perfectly legal.  This would apply to intercoms, wireless networks for data, wireless sensors, etc.   I've heard stories of boats with wired headset jacks at the bow and up the mast... If you are using this headset for team racing, between boats on a team.  That also could be problematic. 

Rule 41 allowed intercom on the boat. Forbidden is to transmite or recieve any kind of message/data ec between outside and the boat.

Intercom allowed. Boat to boat transmisson forbidden.

Team Racing Rules appendix D

Add to rule 41: ‘However, a boat may receive help from
another boat on her team provided electronic communication is
not used.’

I'd say that if the Bluetooth originates on the boat, the BOAT did not receive a transmission.

If your Organizing Authority/Race Committee wants to clarify it - they can add a technology/electronic communications provision to the Race Documents specifically saying what is allowed and what is banned.in a particular regatta.

This seems to be a case of over-writing the rules.  Outside assistance is already prohibited.  The rule as written also prohibits calling your elderly grandmother to check on her health or calling your child to let them know you'll be home a little late.  Plus, as indicated in this thread, it creates confusion over legitimate uses of wireless tech.  What about a wireless wind sensor? Banned?

Unless I'm missing it, the 'rule' that started this discussion is not in the RRS (I did search electronically).  I found it in Appendix K (Notice of race guide) and Appendix L (Sailing Instruction guide) of the 2017-2020 version, but could not find it even in the appendices of the 2021-2024 version. 

The restrictions on outside assistance obviously apply, and some clubs choose to add their interpretation of how electronic communications would be considered.  Locally, one discussion topic was whether 'freely available to all boats' meant 'free of charge' (boats with deep pockets could use satellite communications to download large files that were free of charge - but the airtime is not) or just accessible to all boats (eg downloading a small grib file from an inexpensive subscription service that is accessible to all who pay the subscription).  One approach taken to this is:
 

RRS41 does permit receipt of communication, albeit in very specific circumstances ('unsolicited information from a disinterested source, which may be another boat in the same race'), so there is no absolute prohibition.