As of today the desktop mode has not yet been officially released in the stock android. On GrapheneOS the screen mirroring through HDMI works but it's very far from replacing a desktop/laptop experience IMHO, even with keyboard and mouse attached. By default the connected screen's resolution won't be utilized which will result in empty spaces. There's a workaround but I don't bother.
Personally I use a laptop for everything requiring more screen real estate like coding, office work and browsing.
On GrapheneOS I keep all the apps like finance, identity, messaging and some productivity which I trust to run more securely on GOS compared to the desktop OS. I keep everything in the main profile out of convenience. I use Proton suite to sync the photos, email, notes and passwords between the devices. I find the Proton Drive app to struggle when syncing large files (a backup of few GB). Not sure if the absence of Google Play Services is a problem. A workaround is to transfer them through USB to a desktop where the Proton Drive will sync but it's an extra hassle again.