That's harder on Linux, with Windows I usually had to only copy appdata for the user and everything would be flawless. I don't know exactly what's different with Linux Vivaldi installs, but it almost always breaks like this.
There are Singleton lock files in .config/vivaldi[-snapshot] that can be deleted if the profiles aren't protected by a keyring.
If the profiles are protected by either KWallet or Gnome-libsecret, you need to unlock that keyring before starting Vivaldi. If you moved to a KDE or Gnome desktop environment from something like Niri or Hyprland, or vice versa, this can happen.
With Vivaldi closed, back up ~/.config/vivaldi/ or ~/.config/vivaldi-snapshot, then try launching with the original backend:
vivaldi-stable --password-store=kwallet6
vivaldi-stable --password-store=kwallet5
vivaldi-stable --password-store=gnome-libsecret
vivaldi-stable --password-store=basic (only if the original profile used it; not recommended for regular use) I had to do this when I went from Hyprland to KDE Plasma and KDE Wallet made it so I couldn't open Vivaldi when I logged into the Hyprland session.
For KWallet/libsecret, the original wallet must also be available and unlocked.
It was about how the default keyring was called, and that the name of the keyring ia actually case sensitive.