You could also manually add the record in the C:\ProgramData\KIM\kim.xml
file. Your entry would look something like this:
<item>
<guid>6eb50de2-df37-4743-b5e2-72e71463522b</guid>
<url>http://localhost</url>
<name>K12 Site</name>
<version>12.0</version>
<path>C:\Websites\kentico12</path>
<created>2022-04-07T12:14:49</created>
<hotfix>29</hotfix>
<showlist>0</showlist>
<netversion>0</netversion>
</item>
You'd need to make sure the hotfix is what your current site is at. Again, keep in mind, the KIM for v12 or v13 will work. It's smart enough to manage that because all of the KIMs use the same file just operate off the version node.