Can I add non-cited reference to bibliography?

If an idea or a statement is novel and it's appearing for the first time there is nothing to cite. Anything else needs to be cited. And don't add any citations in the bibliography which you are not citing in the text. Otherwise the reader will wonder why you didn't cite it.

My writing rule is that I list in the bibliography only what I indeed cite. Bibtex helps there a lot.

But if you want to provide some further reference to the readers, then why not just cite them? Like,

The reader might find the works by Spongebob, (1749); Patrick and Star, (1997); Squidward et al., (2018) useful.

just more sane.

It depends on the style you are following. I like this APA style blog post

For many students, the purpose of the reference list is to prove that they completed the assignment. They were assigned a research topic; they researched the heck out of it; and the reference list is there to demonstrate their hard work.

The blog goes on to differentiate the difference (at least in their opinion) between an APA style reference list where everything that is cited is in the list and everything in the list is cited and a bibliography (e.g., Chicago Manual style) where there can be things that are not cited.