TLDR: No, you can't access data from other Chrome extensions from yours.
To do pretty much anything with Chrome Extensions, you need to declare what permissions your extension needs in its Manifest file.
Here is the list of available permissions as of Manifest V3.
There is no permission that relate in a way or another to accessing other extensions' data. From this, it is safe to say that it cannot be done.
And it makes sense: while Chrome does support package dependencies (see here), it does not support other extensions dependencies.
How would your extension even react if another one it depends on is missing? Would it forcefully install it? Would it throw an error? It could lead to lots of issues.
So no, you can't do that.
However, you might want to try to look if the extensions you want yours to depend of are open-source or if they exist as a usable package somewhere.