After nearly a decade of work — with proposals, proofs-of-concept, discussions and other contributions by the broader web developer community — the CSS Working Group has finally laid some of the groundwork needed for container queries to be written into a future edition of the CSS Containment spec! For more details on how such a feature might work and be used, check out Miriam Suzanne’s extensive explainer.
Hopefully it won’t be much longer before we see a robust cross-browser implementation of such a system. It’s been a grueling wait, but I’m glad that it’s no longer something we simply have to accept as an insurmountable limitation of CSS due to cyclic dependencies or infinite loops or what have you (these are still a potential issue in some aspects of the proposed design, but I have faith that the CSSWG will find a way).
Media queries aren’t designed to work based on elements in a page. They are designed to work based on devices or media types (hence why they are called media queries). width, height, and other dimension-based media features all refer to the dimensions of either the viewport or the device’s screen in screen-based media. They cannot be used to refer to a certain element on a page.
If you need to apply styles depending on the size of a certain div element on your page, you’ll have to use JavaScript to observe changes in the size of that div element instead of media queries.
Alternatively, with more modern layout techniques introduced since the original publication of this answer such as flexbox and standards such as custom properties, you may not need media or element queries after all. Djave provides an example.