The population is not a match, but States in the US are by design far more autonomous than "provinces" in other countries. When the original 13 states formed the US they thought of it much in the same terms that member states of the EU think of themselves today - not an identical arrangement, but very similar in spirit.

California (and the other US States) have their own labor laws, their own environmental standards, their own transportation and energy departments, their own distinct safety net programs, even their own militaries! (aka the "national" guard)!

Further, the Federal Government is specifically limited via the 10th Amendment to only those powers which are enumerated to it. By default, legal power is held by the states, not the federal government. This is very unusual.

Every "country" has a different mix of systems and different degrees of local autonomy, but US States are at the very high end of local authority while the federal government is at the low end. Thus, comparing some European nation to the US Federal Government is often misleading as it implies that the US federal government even has the power to do things that a European nation can do, which is frequently not the case, or else is greatly complicated by needing state participation and approval.