Background: I was creating designs using components from a design library (let's call it Alpha design library/Alpha DL). Alpha DL is a common design library used across multiple products. Different variable modes with unique colors were defined for each product and labeled as 'Brand'. Whenever I created a wireframe, the components pulled in from Alpha DL had the default mode, which I then overrode at the page level by selecting the brand pertaining to my product (e.g., Product G).
Current Situation: We now have our own design library (let's call it Beta design library/Beta DL) with a single mode variable collection and published components. I created a new work file within the same Figma project using Beta DL, which is separate from the team and project where Alpha DL resides.
Problem: Every time I copy and paste any design from a previous file into my new working file, it defaults to the properties of the Alpha DL mode. In the variables options, I do not see the variables I created in Beta DL. Consequently, I need to manually select the color from Selection colors, choose Beta DL, and override it.
Ask: Is there a way to make the brand color variables defined in Beta DL the default in all files/pages/designs I create within this project? Alternatively, is there a way to change the automatic file from which the variables are picked up? Is there a specific method to define the variables to achieve this?