I had the same issue too.
Antigravity itself told me its because WSL is headless and is missing the OS keyring to save the CLI tokens in.
I managed to fix it by installing gnome-keyring.
sudo apt update && sudo apt install -y dbus-x11 libsecret-1-0 gnome-keyring
And then adding this to my .bashrc to start the keyring service
if [ -n "$BASH_VERSION" ]; then
export $(dbus-launch)
eval "$(echo "" | gnome-keyring-daemon --unlock)"
eval "$(gnome-keyring-daemon --start)"
export SSH_AUTH_SOCK
fi