See the SAGE Budget and eGC1 Shared Access Data user guide article for details.
Any person with access to the eGC1 can view its connected budget, but users with access to the budget must be granted explicit permission to the eGC1 in order to view it.
A person’s ability to edit a connected budget is determined by the access they are granted to that budget. If a person with access to the eGC1 has not explicitly been assigned access to its connected budget, they will be able to open and review the budget from the eGC1, but they will not be able to edit it.
Anyone with access to the budget can verify their access to the eGC1 by looking on the History tab of the budget. At the bottom of the page, click the + sign to expand the pane for the Budget Period connected to the eGC1 you want to access, and then click View eGC1. If you do not see the View eGC1 link, it is because you do not have permission to view the connected eGC1.