I'm not sure what's different about my setup (just a Vaultwarden deployment hosted behind Tailscale, connected using the official Chrome extension and Android app), but I've never once encountered the long unlock delays due to sync attempts. It's always unlocked instantly. And the app is frequently unable to connect since I'm not always on the tablet.
I use Vaultwarden because I need something cross-platform (macOS and Linux) and with support for passkeys.
The idea of using different storage methods for different categories of passwords is very interesting. Maybe I don’t need rbw (the rust reimplementation of bitwarden CLI) in my server and something simpler/different could do the job