The OP here is mistakenly interpreting dedicated as loyal, faithful, determined, devoted. But in the context of a dedicated team the meaning is exclusively allocated, not assigned to anything else.

Merriam-Webster dedicated

1: devoted to a cause, ideal, or purpose : ZEALOUS
a dedicated scholar
a novelist with a dedicated following

2: given over to a particular purpose
a dedicated Web server
The fees would be put into a dedicated fund for rebates that go directly to households and employers

Being a "dedicated team" implies nothing at all about how "committed" the members of a team are to their work. It just means they only work on whatever project they're "dedicated, exclusively assigned" to. Syntactically, you might reasonably say...

I manage a dedicated API integrations team
We're a team dedicated to API integrations
Our a team is dedicated to API integrations
etc., etc.


EDIT
I didn't intend to imply that "a dedicated team" always implies "exclusively allocated" rather than "devoted" - but it usually does. In a context such as the exceptionally common sequence set up a dedicated team, I would be astonished if anyone could find an example of that particular sequence having the latter sense.