This is an interesting case! I might recommend you create one master project that holds all budgeting tasks. In this project, you could add a customer field specifically for budget. Every department roadmap planning project can have it’s budget requests, which are multi-homed into this master project when formally making the request. I might even recommend creating a master budget request inbox to help you build a process for requests, then once approved, you move that request task to the finalized budget project to serve as the ultimate source of truth.
Use sections to break apart each dept or initiative request or approved budget ask, depending on how you organize those requests. Additionally, to gain a total sum of numerical values for those tasks, multi-select the tasks in each section, and the sum total will appear in the Task side pane to the right.
it’s not perfect, but it is possible! That said, our team is actively working on improving the sum/custom field addition function of custom fields in Tasks, so this process will only get better with time.
In the meantime, I hope this helps!