"Unlawful sexual intercourse" like in your California example is fine: that's a good way to word sexual activity that's illegal without conflating it with violence.
Generally, that meaning is sex without legal consent. Most state rape laws include sex with adults lacking capability for consent (due to intoxication, disability, etc.), even if they happen to carve out lack of legal capacity to consent due to age to a separate section of law, and do not require violence beyond the violence inherent in sex without consent, though they certainly include nonconsentual sex acheived through violence.
So, while it may or may not be carved out for organizational or other reasons in particular criminal codes, there is no reason that “statutory rape” does not fit conceptually within the space of “rape”. (The phrase “forcible rape” already exists for the subset you seem to want to limit “rape” to identify.)
“Statutory rape” isn't usually the term in the law, it's a common-language hedge to indicate that it was (at the time the term was coined) literally rape under a particular set of criminal statutes, but not what some people consider “real” rape.
In some statutory schemes it is exactly rape still, in others it has different formal names (“unlawful sexual intercourse” [Penal Code 261.5] in California law, for instance.)