I am looking to display content in the built-in HTML module based on a user's role in my organization, with the ability of users to edit content specific to their role. Would the built-in module have support for this feature, or would I need to develop a custom module for this purpose?

Yes, I realize that I can target visibility to certain user groups. However, would I be able to provide separate content to each user group within a single module. For example, can the sales team have separate content from the marketing team within the same module, and be able to edit their content accordingly? And would there be a way to enable, say, the sales team to view the content from the other teams as well, but have the startup focus be on their own team

For content modules, you would have to put multiple ones on the page and control their view/edit permissions in the module settings. The page could be crowded if you are a top level admin, but the content editors that are assigned to a module wouldn't know.