@ania_roh YouTube web part in SharePoint works with link to video or embed code. So, you have to give the link of your latest video from YouTube.
Now, this is not specific to SharePoint. So, you have to find a way to get the URL of latest YouTube video & add it to the web part on SharePoint page. You can check in Google/YouTube documentation if there is any shortcut URL using which you can get the URL of latest video from your channel.
I found this solution online to get the URL, try this & see if it works for you (refer image below as well): How to link to the most-recent video from my own YouTube account?
Documentation: Use the YouTube web part