Just thought a topic here might help others looking for information about this.
Youtube have made a change that has broken a lot of 3rd party applications including the Kodi Youtube Add-on. See this thread on the Kodi forums for more info.
It appears that devs will already be aware of this so hopefully they will come up with a fix. Discussions on other projects with the same issue seem to indicate that a solution should be possible.
EDIT: Looks like the add-on developer anxdpanic already has a solution for this. At the moment it’s a beta version (6.5.2~beta2) and I believe you need to install it from the ZIP file.