I wonder how ChatGPT or Claude are actually GDPR compliant, but Apple has problems with Siri.

What's to wonder. Those third party apps are not part of the core OS and others apps can't access them.

I'd instead wonder why Google and Microsoft seemingly don't have to comply with the DMA.

Because this is not related to the GDPR at all, but the Digital Markets Act (DMA). It's purpose is to enable competition and not allow big tech to abuse their market dominance (e.g. in this case Apple not wanting to grant any competition the same access to MacOS so that they don't have to face competition for Siri AI).

This isn't GDPR, it's DMA. They're not subject to it.