I don't think this is about grammatical gender. Though I won't pretend to know enough Japanese to go into a full linguistical analysis, Japanese does have a whole spectrum of words for the first person singular and their usage depends on lots of factors. Some of which clearly indicate whether the person speaking is male or female. Using those incorrectly will cause amusement for the native speakers.
Very true. But those are connotations which refer to natural gender, which more often than not has nothing to do with grammatical gender (this is very apparent in languages such as German). Japanese grammar still does not include grammatical gender. Same goes for English, too.
Japanese has around 18 words for 'I' and as you say they are not about gender, but most are almost exclusively used by one gender.
'Watashi' / 'watakushi' - the standard is used by both genders professionally, but rather uncommon for males privately.
'Boku' is predominantly male 'I', but is very common for women to use when singing.
It's very much context what you can and cannot use.
It depends if you include slang/archaic ones, but on the top of my head:
watashi, watakushi, atashi, atakushi, atai, uchi, wacchi, washi, boku, jibun, wagahai, sessha, yo, oira, ware, chin
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'Watashi' / 'watakushi' - the standard is used by both genders professionally, but rather uncommon for males privately.
'Boku' is predominantly male 'I', but is very common for women to use when singing.
It's very much context what you can and cannot use.
watashi, watakushi, atashi, atakushi, atai, uchi, wacchi, washi, boku, jibun, wagahai, sessha, yo, oira, ware, chin