The plugin prevents the Bricks builder backend

I use the Bricks Builder on many sites. To prevent hot linking issues, I installed the Bunny plugin and set it up with a custom subdomain. Everything works fine on the frontend (including hotlink prevention). However, it prevents the Bricks Builder from running and gives me an error message:

Session expired

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That error message is a known issue when a cache plugin tries to cache the backend and the Bricks Builder specifically. But I disabled the builder and turned off the plugin for logged-in users. The problem persists. There are no other caching plugins installed. If I disable the plugin, it works. Once it is enabled, the error gets back. Logging in again doesn’t solve it, it keeps asking to log in.