Is it possible to embed a TLS certificate into an application or hide it somehow so that it’s not so easy for a user to just export it from cert manager on Windows? Or does all certificates have to be stored in the manager?
This means that yes, you can store in the program code certificates, private keys and anything else you may find it useful for the program to work the way you want.
But it's not secure.
Storing critical information (e.g. access keys) where a user has read access to and expecting that the user won't find it, has been tried many times in the past (a notable case being DRM) but has failed in every case.