I've noticed similar issues lately. In fact, I have resorted to keeping my my Pocket browser extension in Brave disabled because for whatever reason, Pocket seems to cause the browser to fully utilize ~1.5 cores. I only discovered this after disabling all extensions and using them one at a time. Pocket was the only one that seemed to have a consistent signal. I haven't had weird Brave CPU spikes since I disabled Pocket.

I've wondered about how to exfiltrate all of my accumulated links I've put into Pocket over the past ~7 years or so.