I think a good example is actually The Lord of the Rings. As we know, the backstory is massive, yet the novel starts right in on the action without introducing the world or its history or mythology first. We learn about that through the explanations the characters give each other and of course by their encounters and interactions with that backstory.
You might object that The Hobbit was written before The Lord of the Rings and that it serves as its backstory, but I read the LotR without having read the Hobbit and found it completely comprehensible.
There are sections in The Lord of the Rings that are entirely backstory, without any (inter)action of the protagonists, but these are told in an entertaining way, embedded in a fitting situation (e.g. while the characters rest), never too long (for my taste), and in fact contribute to this type of worldbuilding story, which partly becomes interesting through backstory alone.
Even if this is not a contemporary setting, I believe it is a good example, because it illustrates the importance of what type of text you are writing: your genre and writing style. In some genres, like historical or crime fiction, the readers expect a certain amount of background information. A sleuth is expected to uncover what went on before (which is actually a great device to organically divulge it), and every novel set in a time before our own takes part of its appeal through extended descriptions and meandering side stories.
Good examples in contemporary settings are countless. Just read any well criticized book. They all contain some amount of backstory, and it is less a matter of how to elegantly explain the backstory, but rather how to elegantly write in general. For example a sentence like "On his way home from work ..." already tells you that this person has a job. If that is not a great example of literary writing, then not because it contains backstory, but because I'm unable to form pleasing sentences.