Problem: Can we control other Software's Post Types with Toolset, so we could, for example, change the Post Types settings, such as add hierarchical true, or maybe remove archive true?
Solution: The only way to control other's Post Types with Toolset is to actually replace those with Toolset. https://toolset.com/faq/how-do-i-convert-existing-custom-types-and-fields-to-types-control/
That may be a solution in cases where the other software later can be removed - as otherwise the Post Type would be registered twice. It is no solution when the other Software strongly relies on this Post Type and its settings. How strongly that software relies on such settings of Post Types depends on the software, it's best asked to the support offered by 3rd parties.
You can always easily set any post type into a relationship, as there, the post type does not need to be created by Toolset, to work. Also, you can display such data with Views easily, as long the post type is not fully hidden to the public.
This is the technical support forum for Toolset - a suite of plugins for developing WordPress sites without writing PHP.
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