Applying for a postdoc. Should I mention that I completed my PhD with no supervision?

Should I mention that I completed my Ph.D. with no supervision?

Definitely not. "I had no supervision during my PhD." could be interpreted as "Nobody taught me anything during my Ph.D. so I am unqualified." or "I am incapable of giving credit to other people who deserve it." or "I am so obnoxious my supervisor will not interact with me." or "I refuse to work with others." It is likely none of these are true, but the misinterpretation is a possibility.

What should happen is that your supervisor writes a letter of recommendation saying that you have shown a high degree of independence and that you now have more expertise in Y than they do.

Tread carefully to avoid a doesn't play well with others impression.

I was in a somewhat similar situation (Ph.D. supervisor in a different area), although I had plenty of contacts in my own area. In my applications, I never explicitly brought this up but did claim that I was rather independent in setting and pursuing my research goals. The evidence I brought up was here's some single-author paper and here's a bunch of papers coauthored with all sorts of different people. I left it to the letter from my supervisor to say anything more because he is in a much better position to put this positively.

You shouldn’t say it, because it’s not true.

Of course, I’m guessing here and this isn’t based on any specific information in your post, but “my supervisor didn’t advise me on the mathematics in my thesis” is not the same as “I received no supervision”.

I am fairly confident that your supervisor taught you many things about X, the philosophy of doing research in math/theoretical physics, career advice, productivity and writing tips, and probably other things. Those workshops you attended - how did you hear about them? How did you obtain funding to attend them? Was your supervisor really so “laissez faire” that they gave you no assistance whatsoever related to anything that you can attribute your success to? (In that case, in what sense were they your “supervisor”? And why do you like them?)

To summarize: I congratulate you on your independence, but this quality is best attested to by others. Be mindful of how things you say about yourself are perceived by others. When you say you received “no supervision”, it sounds like you’re saying you got no help. But everyone gets some help along the way, and denying that, or appearing to deny it, makes you sound petty and ungrateful.