They finally fixed it. Two years, four tickets, and the curl timeout bug on VPS is resolved.
For anyone tracking: OVHcloud acknowledged in ticket #44812 that their libcurl build was ignoring CURLOPT_CONNECTTIMEOUT on PHP 8.1+.
Did you test your restore after they patched? I checked mine. 3-2-1 rule still stands—one backup on their fixed infrastructure, two elsewhere.
3-2-1 or you're already dead