Many thanks for the update @pandebcn. From the checks I performed on your site, I suspect this is host related. One of the reasons I suspect so, is that your site seems to have some geo blocks when I try to access it from some regions. I can also see various Litespeed related optimizations performed, which could also be contributing to the issue.
To troubleshoot this further, rather than whitelisting any ID rule, can you temporarily deactivate ModSecurity before attempting Site Kit set up once more? If this isn’t possible, can you share what specific rules were whitelisted? Your site needs to be able to communicate with sitekit.withgoogle.com, and I can provide you with some cURL commands to see if you are able to communicate if you wish.
In addition to performing the above check with ModSecurity temporarily deactivated, can you share a screen recording of your experience when attempting Site Kit set up? Please do so from a Chrome browser incognito window, while also having the developer tools window open displaying any console errors. You can use a service such as Loom to share a screen recording, while using the same form previously used to share this privately if preferred. Thank you. ?