Dynamic Link between PP and AE not working when build numbers don't match

The Versions are:
PP: 24.2.0 BETA, Build 44

AE: 24.2.0. BETA, Build 42 and Build 44 

Mac Studio M2

Sonoma 14.0 (23A344)

You mentioned builds 44 and 42 for Ae and Pr, respectively. But you did not mention what versions those builds are. If you know your Pr and Ae installs are compatible but you're still unable to Dynamically Link between the two, then you are experiencing a bug that we need to know more about. Steps, build versions, and some basic system specs are all things that could help us figure out why it's not working for you.

Turns out, even when the build numbers match Premiere randomly decides that it will not work with the After Effects Links.

It can be a pain trying to keep everything in sync all the time, but the CC Desktop app makes it a lot easier than it used to be and it's still better than having to render and export everything before moving from one app to another. You can find more information here about using Dynamic Link in Pr, Ae and Ch:
https://helpx.adobe.com/after-effects/using/dynamic-link-effects.html