In src/common/pico_sync/include/pico/critical_section.h, critical_section_is_initialized is placed in the documentation group mutex instead of critical_section:
/*! \brief Test whether a critical_section has been initialized
* \ingroup mutex
*
* \param crit_sec Pointer to critical_section structure
* \return true if the critical section is initialized, false otherwise
*/
static inline bool critical_section_is_initialized(critical_section_t *crit_sec) {