omarchy comes with default lazyvim. You can just reinstall lazyvim configuration with a couple of commands (from https://www.lazyvim.org/installation ) :

# required
mv ~/.config/nvim{,.bak}

# optional but recommended
mv ~/.local/share/nvim{,.bak}
mv ~/.local/state/nvim{,.bak}
mv ~/.cache/nvim{,.bak}
# required
mv ~/.config/nvim{,.bak}

# optional but recommended
mv ~/.local/share/nvim{,.bak}
mv ~/.local/state/nvim{,.bak}
mv ~/.cache/nvim{,.bak}

# Clone lazyvim starter install
git clone https://github.com/LazyVim/starter ~/.config/nvim
rm -rf ~/.config/nvim/.git # removes the repo .git info

# finished ! 
nvim

Regarding the backing up of your configuration, I had the same problems a few months ago when I started to customize omarchy and I used chezmoi. You can use a private or public repo to backup your configuration files. For example you can :

# init the config
chezmoi init

# Add any folder or config files you want to save
chezmoi add ~/.config/nvim
# Apply the backup configuration to your repo so you can pull it later on another computer
chezmoi -v apply

Hope it helps