How to create and log into different organizations with one account?

[NOFWx]

I'm self-employed, have Microsoft 365 Business Basic, and interact primarily with two different companies. To keep my communications between these two separate, I've created two tenants in Azure, intended to serve as the organizations (in MS Teams) corresponding to these two companies. This is how it looks like in Azure:

However, I can't figure out how to actually use these new organizations. I was expecting for the Teams interface to allow me to switch between the organizations, as seen here in another (personal) account of mine:

This personal account is part of five different organizations, some created by me, and some by others, and I can switch organizations as I wish by clicking on my profile picture. On top, whenever I log in at teams.microsoft.com, I automatically get asked which organization I want to log in with.

Not only do I not seem to be able to switch organizations like this using my business account, I don't even see a way to log into these new organizations at all.

Logging in with my primary handle username @org1.onmicrosoft.com only gives me access to Org1, and when trying to log into e.g. Org2 with username#EXT#@org2.onmicrosoft.com, which is the handle that Azure shows me for Org 2, I just get an error message.

In short, I just want to be able to do what I've been doing with my personal account all along – log into multiple organizations with just one username and password, and be able to switch organizations with the click of a button. How do I set that up?

Thank you in advance!

[#2]

@NOFWx You don't need the Orgs in Azure.

Your Azure AD account is hosted in your primary org and then can be a guest in other orgs, it just needs to be invited to those orgs. Then you will get the ability to switch between Orgs in Teams.

[#3]

Thank you @Steven Collier! Just to be clear though, those other organizations I want to be part of should still be under my control. So I don't just want to be a guest in my client companies' orgs, I want to create my own orgs, e.g. one for all the people I work with at company A, one for all the people I work with at company B, and so on. Does that make sense? In the screenshot from my personal account, you can see that out of the five orgs, I'm only a guest in two of them, the other three are my own. That's what I would like to have.

And the problem is, I can't seem to be able to invite myself into orgs that I created in Azure. If I go to Org2 in Azure and try to invite my primary handle (...@org1.onmicrosoft.com) as an external user, I get the error that this username already exists in this directory, even thought the list of users only shows my secondary handle (...#EXT#@org2.onmicrosoft.com) with which I can't log in or do anything else.

[#4]

I think this was a misconception on my part. Even the orgs which do not have the "(guest)" designation are not necessarily owned by me, it just means that I'm a member and not just a guest.

Somebody correct me if I'm wrong, but it seems like one cannot own/manage more than one organization using just one account. So a workaround for what I originally wanted to have would be to either have all communication in one org, distributed into different channels, or to create as many orgs as one needs using additional MS business accounts, and for each of those orgs add the primary handle as an external member and the clients as external guests.