Thanks so much for all the tips and suggestions, I finally got my logo and all URLs switched over correctly. Below the Recipe

# 1. Exec into the container:
docker exec -it client1-wordpress-website bash

# 2. If WP-CLI isn’t present, install it:
curl -O https://raw.githubusercontent.com/wp-cli/builds/gh-pages/phar/wp-cli.phar
chmod +x wp-cli.phar
mv wp-cli.phar /usr/local/bin/wp

# 3. Verify installation:
wp --info

# 4. Search & replace your old test domain → live domain:
wp search-replace 'client1.mydomain.de' 'client.de' --skip-columns=guid --allow-root

# 5. Update the Site URL and Home URL:
wp option update siteurl 'http://client.de' --allow-root
wp option update home    'http://client.de' --allow-root