Licence supply is not the same as a migration
A supplier change concerns who supplies and bills the licences. A tenant migration moves services or data between Microsoft environments. Those are different projects. You should not need to move email or SharePoint merely to compare a licence quotation, but the actual supply route must be checked before anyone promises a particular outcome.
Existing IT support can remain with your internal team or current provider if that arrangement still works for you. First separate the licence line from bundled backup, security, helpdesk and other services. A lower licence price does not by itself make an entire managed service cheaper or equivalent.