I Built a Chrome Extension to Sync AI Studio System Instructions. Here's Why chrome.storage.sync Couldn't Do It

I use Google AI Studio on three machines. My laptop, my desktop, and occasionally a work machine. Every time I switched devices, my system instructions weren't there. I'd carefully crafted a "Software Architect" prompt, a "Posts & Content" persona, a "YT Expert" context — and they existed on exactly one device. The others were blank. Chrome sync handles bookmarks, passwords, even open tabs. Why not this? The Obvious Solution That Doesn't Work chrome.storage.sync looks like exac...