Repository owners can delete issues and comments, but no, issues should usually not be deleted. If they are no longer needed they can be closed, but keeping them around can still be useful for future reference.
If content needs to be removed e.g. because it contains sensitive information or because it contains harassment, then individual comments can be edited, hidden, or deleted by people with write access to the repository. See: Managing Disruptive Comments on GitHub Docs. Similarly, log files of Actions can be deleted. Admins of the repository can delete entire issues, but you can't necessarily delete the issue yourself.
As a more general point, open source projects are public spaces. Stuff is public by default, and the internet never forgets. Some tools such as GitHub make it possible to hide or delete comments within the scope of the platform, but other media like mailing lists do not. And scrapers gonna scrape. Sometimes open source projects offer private channels e.g. to discuss security issues, but this isn't the norm. Git commits are also immutable and stored decentrally. If someone has pulled your commits, you can't edit or delete their copy. Note that commits typically contain your name and email, so publishing your work has privacy implications.