Is the New Neighbears DLC transferrable across platforms? (Cozy Grove)

Unfortunately, no. Each platform will check with its app market to confirm ownership before allowing you to use the DLC, so you have to own the DLC on the platform where you want to use it.

Note that players on Apple Arcade get the New Neighbears DLC for free as part of their Apple Arcade subscription, so they automatically own it on their Apple Arcade installations. But they don't automatically own the New Neighbears DLC on other installations (e.g., if they also have Cozy Grove on Steam).