I write a lot of documents based on AI transcriptions, and it sometimes mis-identifies the gender of the speaker. Before I embark on trying this from scratch, I wonder if anyone has created a macro that will take a block of plain text from the System Clipboard, then change all gender pronouns from male to female or vice versa. For example he -> she, his -> hers, him -> her. Keeping capitalization intact.
Bonus points if the script identifies the gender first, otherwise there might need be two scripts.
Making such a macro for yourself really shouldn't take long, I think. Just use multiple Search and replace actions. Someone may have a more elegant method, but that would get the job done without too much work.
The answer in terms of traditional grammar is that your third column there is for plural (or for unknown gender of person) and that the table omits it/its/itself (neuter). The examples after that are personal sociopolitical choices which can be as varied as proper names, and so which are outside the practices of the established grammatical system – as well as not being relevant to what the OP asked for.
Many grammatical resources are available on the Web, and I would recommend them over what any chatbot may tell you.