I think that was a move in VP direction. Especially since she is probably one of better choices for Biden's VP, because she brings plenty of new people to the table and she is decent contrast to him. Plus as you probably already know this time VP will have much bigger role than usually (due to the age of the candidates). Therefore this doesn't necessarily have to be a miss on her part.
I think she was offered an ambassadorship or some other prestigious position involving foreign relations. I doubt they will offer her VP, as she still is seen as divisive by a lot of the dem establishment. They see her as a loose cannon and won't want her next in the line of succession. Ambassadorship is a nice carrot to dangle because she gets to do what she loves doing (meeting with foreign leaders, negotiating, travelling a lot) whilst effectively being defanged and removed as a real threat to the Democratic establishment. It's a win-win for both the DNC and Gabbard.
Here's my guesses at what Biden's been offering in return for endorsements:
Kamala Harris - Attorney General (most likely) or VP
Elizabeth Warren - will be offered Secretary of Education or VP if she endorses Biden. I think she's holding out in hopes of being VP nominee
Andrew Yang - Secretary of Labor OR Secretary of Commerce
Tulsi Gabbard - Ambassadorship, National Security Advisor (most likely), Secretary of State, or some other position heavily involved in foreign relations
Bloomberg - Federal Reserve Chairman
Pete Buttigieg - Chief of Staff?
Most of these people will serve about a year or two before resigning to springboard themselves for eventual runs for other offices. This is fairly common for early cabinet appointees to serve a year or two before then moving on to some other job or focusing on campaigning for office. A couple years in a presidential cabinet is basically a way to pad resumes and get "experience" they can tout when they later run for elected office--Buttigieg especially needs this to fight off criticisms of lack of experience when he runs for President again (which he likely will in 2028 OR 2024 if Biden decides to step down due to age).