From a philosophy of language perspective, pronouns don't by themselves have any truth value, they function to refer.
I disagree. Pronouns like "that" and "this", "you" and "they" are simply refer functions, but in English at least gendered pronouns like she and he carry additional information, and therefore can be used to misrepresent aka lie.
You missed that you implicitly assumed the meaning of "Debbie is cold, she asked for a blanket" is what it always has been, but implicitly accepted the meaning of "she" has been changed.
If we write out those assumptions and simplify, we get:
"If we assume "Debbie is cold, she asked for a blanket" can only ever mean that the person known as Debbie asked for a woolly cover, and assuming that said person Debbie did indeed ask for a wooly cover, it is not a lie to say Debbie asked for a blanket."
"If we assume "she" could mean a biological man or a biological woman, amd Debbie is a biologically male transwomen, it is not a lie to say "Debbie is cold, she asked for a blanket" because this means "Debbie is cold, she, the person I just referred to who could be of either sex, asked for a blanket"
Well, no shit Sherlock 😂
However, if we do not assume "she" could mean a biological man or a biological woman, and keep to the original sex based meaning, we get "Debbie is cold, she, the person I just referred to who is a biological woman, asked for a blanket"
And that is a lie because Debbie is not a biological woman.
Do you see? The flaw in your logic/philosophy is that it pre-accepted the thing you are trying to prove.
It's nothing to do with philosophy of language, it's simply an error of logic. You have the wrong frame.
It is that initial implicit asdumption "she" could mean a biological man or a biological woman which is the contested belief at the heart of all this so it is that which you need to interrogate, not what comes after.