As a part of project scope we have to deliver to the Client digitized data sets – some houses and roads. Can we use Mapbox Satellite global imagery layer  under Professional plan  for feature digitizing?
No. You need a Mapbox Commercial Satellite licence.
You may trace Mapbox-hosted imagery in order to produce derivative vector datasets for non-commercial purposes, and for OpenStreetMap. If you wish to produce derivative vector datasets from imagery for commercial purposes, you must buy a Mapbox Commercial Satellite license.
On that page it says:
Commercial Data Ownership
Any vector data you extract is owned by you. You can do anything you want with it — sell it, use it privately, open it up to the world, anything — forever. You'll have 100% ownership and control of your data and any vector derivatives are your own intellectual property. No restrictions.