Can neighbour hear my bluetooth headset?

Can a neighbour with a bluetooth headset hear my TV's bluetooth emission through a wooden wall?

If you're asking about if the signal can get through, then the answer is yes. To block a bluetooth signal you'd need very thick and dense walls (something like thick concrete walls) or something that acts as a Faraday cage.

Usually bluetooth transmissions are encrypted by default, the security on this mainly relies on the pairing method.

But as forest commented, you shouldn't be worried about anything. Statistically speaking I think that it's quite unlikely that your neighbour would have the cryptographic expertise to hear your transmissions.

In August 2019 information about a Key Negotiation of Bluetooth (KNOB) Attack was published.

At this point it's best to assume that all of your Bluetooth devices are unsafe, unless you upgraded firmware in 2019:

After we disclosed our attack to industry in late 2018, some vendors might have implemented workarounds for the vulnerability on their devices. So the short answer is: if your device was not updated after late 2018, it is likely vulnerable. Devices updated afterwards might be fixed.