I'm unable to find anywhere online where it states that BizTalk Server 2010 is supported/not supported fully by Windows 10.
No, not even BizTalk 2013 R2 is supported on Windows 10 as can be seen at Summary of 64-bit support, operating systems and SQL Server versions supported by BizTalk Server and also Hardware and Software Requirements for BizTalk Server 2013 and 2013 R2 as it is not listed on either page as a supported operating system.
There is a related question about BizTalk 2013 R2 and windows 10 called BizTalk Server Configuration failing to create group. The conclusion for that is, yes you can run BizTalk 2013 R2 on Windows 10, but as per a answer and comments there it probably will not be supported by Microsoft for a Production environment and could break with updates and patches applied to the operating system.