I can understand your confusion. Podio does indeed have a concept of "workspace contacts", but we have been recommending people use apps for years and plan to retire this inflexible type of contact. We also previously had "contacts", now renamed to "connections", as this is simply a list of everyone your connected to on Podio.
As for contacts in terms of clients or leads, you should always use an app for that, and we would recommend that you use the Contact app type for this - see this article here: https://help.podio.com/hc/en-us/articles/201019938-Importing-Contacts-Using-a-Contacts-app
So your conceptual road block is should be cleared by this: Use an apps for Clients and Leads, where they will be created as items. Then use this tutorial to understand and work with apps and items through the Podio API: https://developers.podio.com/examples/items
If I understand you correctly, the same is more or less true for proposals you want to have as Podio projects.