One of the requirements of the DMA is that "the gatekeeper shall provide end users [...] with effective portability of data [...] and including by the provision of continuous and real-time access to such data." (article 6(9)).
Personally, I think that the requirements that the access to data portability needs to be continuous and real-time is a potential explanation of why Threads promises to add ActivityPub.
Keep in mind I'm not a lawyer however, and feedback is much appreciated!