Mr Bass, i don’t know if your question is still relevant after 2 months, but the short version would be as follows:
1. Create a new Google bucket with the name of the subdomain you intend to use, e.g. storage.ioutdoor.com.
2. Google will ask you to validate the subdomain through the Google Search Console in this process. This involves creating a TXT-record in Cloudflare (DNS) with the name storage.ioutdoor.com and the value/string that is provided by the Search Console. After validation the bucket can be created.
2. Create a CNAME record in Cloudflare with the name storage.ioutdoor.com and the value c.storage.googleapis.com
3. In the WP-Stateless settings, set the bucket name to storage.ioutdoor.com, set the mode to Stateless, and set the domain to https://storage.ioutdoor.com (including the https:// part)
Your bucket should now be working, if you already had WP-Stateless set up with a different bucket, you can do a one-time Sync to copy all the files to the new storage bucket.