Core allows you to set up standard budgets in general and then assign them to multiple projects or create budgets specific to a project (parent projects with child phases) from the Budgets screen. You can also create custom and unique budgets for projects in the Projects screen.
In case of 'template budgets' in Core, you can add all the standard budget details that your team uses most of the time and add line items for all the common activities and expenses involved. In the future, you can create new budgets using the Create From Existing Budget option, choose this template budget to copy from, and then assign it to the relevant projects. Check Core Help Center for details.
After logging time and expenses against such projects, you can run the Budget Comparison reports to track their progress.
In case of custom budgets, you can go into the project details and create a unique budget for it so that it is not shared with any other project. Check Core Help Center for details.