Generally, is it better to send recommendation letters or the referees' contacts when applying for a postdoc?
The request to contact by email (without specific requirements) suggests a less formal application process.

I would send a brief email (a few sentences to a couple of paragraphs) explaining your interest in working there and why you would make a good candidate.  The lab supervisor is probably very busy, so by keeping it brief you have the best chance that it will be read.

It would also make sense to attach your CV, so they have a sense of your skills and background.

However, I wouldn't include any other materials (such as a separate cover letter or letters of recommendation) at this stage.  Wait until they express interest in continuing the conversation (and then be led by them about the next steps).

Exception: if one of your referees knows someone at the lab.

In this case, I would ask the referee if they would be willing to make an introduction for you.  This is likely to make more of an impact than you contacting the lab "cold".

Even if the person the referee knows is not the same as the contact person for the job, having the referee contact the person they know is probably the best way to go.