The easiest way is probably to just logon now to the steam account with the business account, then add the new MFA authentication from the personal phone and set that as the default. Once it works with the personal phone, delete the business phone from the account and the authenticator app.
How can I move accounts from one authenticator app to another under a different account?

I have two phones with two Microsoft Authenticator Apps (MAA) registered to two different email addresses. The one is business, and the other is personal.
I have mistakenly added some personal accounts to require authentication from the MAA on by business account, and would like to transfer these to my personal MAA instead.
Example: My personal Steam account requires authorisation from the MAA registered to my previous business Microsoft account, and I would like to link my Steam account to my personal MAA instead, so that when I leave this company I won't lose access to it.
How can this be achieved.