Yep! And engineering advances can trigger breakthroughs in both. It is marvelous to see basic research, applied research and engineering forming a virtuous complex.

Thermodynamics is my go-to example here.

Steam engines came first, and thermodynamics was partially invented to study them. Later on, thermodynamics helped make better steam engines.

Not accurate. Early thermodynamics (in the broad sense, including gas laws) like Boyle’s 1662 Law and others led to Papin’s 1679 invention of the steam digester and related inventions (steam release valve) which directly led to Savery’s 1698 steam engine.

Vacuum science is also a critical predecessor to the steam engine, developed by Galileo in the 1630s and demonstrated as artificial vacuum and the barometer in the 1640s.

Yes, nowadays we systematize and include Boyle's law and others within thermodynamics.

About Vacuum Science: I grew up around and in Magdeburg, which is famous for her (vacuum) hemispheres. https://en.wikipedia.org/wiki/Magdeburg_hemispheres