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Azure DevOps Server makes the process of setting up a new team project very straightforward—so much so that you may be inclined to create a new team project for every software project. I would generally not recommend this; with support for multiple teams and backlog isolation at the team level, it is possible to have a logical separation, along with the ability to share within a team project. In principle, you should consider a team project for each product, and a team for each work stream. The only time you should consider splitting a product team out into a separate team project is if it needs to follow a unique process, since process templates are scoped at the team project rather than at the team level.
If you find yourself organically needing to grow out into a new team project to use a different process template, you can consider leveraging the VSTS Migration Toolkit (https://nkdagility.com/vsts-sync-migration-tools/) to carry out a full fidelity migration.