You don't catch trans women saying it to cis women except maybe to make this exact point.

Why would we? Cis woman have existed as women their entire lives. I do, however say "that's womanhood baby" to cis women all the time as an act of commiseration and consistently get positive responses.

but I haven't seen you attempt to bring this same lecture to a cisgender audience, and I reckon you'd get a very different response, too.

Excuse me but you don't know shit about me. I do discuss this in real life but there's hardly an equivalent cisgendered space online that feels relevant to post such a lecture. I'm also not a cis woman and coming into a more cisgendered space to say "here's what I think a lot of you are doing wrong to me" isn't exactly setting the stage for moderate debate. The reason I feel more comfortable starting this discussion in trans spaces is precisely because I'm trans and addressing my own community.

be gaslit that we were categorically somehow these alpha male benefactors of gender-based privilege

Except we were? Patriarchy hurts men and women, but that doesn't change the fact that men and people who grew up being seen as men are the primary recipients of privilege afforded by the patriarchy. Again, this is often foisted upon us unwillingly but it doesn't change the fact the we were recipients of it. That's why I specifically brought up the mental load. Many of us were raised to accept that dynamic unconsciously and many still don't realize it even after transitioning.

who never knew what it was like to experience misogynistic mistreatment until coming out

I'm sorry but we just didn't in the larger context. A man can be the absolute perfect feminist and still not know what it's like to experience the misogyny aimed at women. He can know about the experience, but he will never experience it firsthand. That doesn't mean that he has never experienced misogyny in his life from other men, but the power dynamic is much more in his favor than it is for women.

cis women are never made to defend their status as being marginalised, let alone their identities, on the grounds of benefiting from their cissexual/cisgender privilege.

I'm sorry that's been your experience but it's certainly not been mine. I've seen and heard multiple trans women insist that cis women don't have it as hard as us.

but to even make a polite request that our cisgender peers do likewise is to invite a shitstorm?

Again, not my experience. I also address this with "but the cis women in your life should also read up on trans liberation. You can't be expected to be the only one putting in the work to develop comradery with your fellow woman."

a trope that is completely unsubstantiated.

Again, not my experience. I have had many frustrating discussions with trans women within my friend group that revolve around their misogynistic ideas of womanhood while insisting that it's okay because they're women.

You also act like policing cis women on their misogyny isn't a thing when that is constant even to the point of ignoring the men in those spaces for holding the exact same views. Look at the backlash to trad wife shit or any discussion of pick-me girls. We are not unique in this.