No, this isn't true, and I think that you (as someone who is not a trans man) should not be trying to claim expertise on this matter.
Trans men do not have a "vested interest in perpetuating [misogyny]": that is absurd.
What form of misogyny benefits us? Genuinely, which one? Is it the idea that women are fundamentally incapable of making their own decisions about their bodies and lives, and that men should tell them how to live? That can't be it; we're denied gender-affirming care and forced back into the closet in droves because we are supposedly hysterical, delusional teenage girls with ROGD who need to be set back on the right path.
Is it that women are overemotional? That's funny, isn't there a lot of fearmongering about volatile, scary trans men on testosterone? The fear of what happens when a winy, tempestuous bitch gets her little freak hands on the violent-man drug? Doesn't misogyny play a part in characterising us as illogical and without restraint?
What about patriarchal obligations to motherhood? Sorry, do you think that trans men have better access to abortions than cis women? From what I've seen, the opposite is true.
Trans men do not have systemic power over trans women in the same way that other groups of marginalised men have systemic power over women from the same communities; trans men aren't out there denying trans women healthcare, or forcing them into arranged marriages, or denying them jobs. We don't even have systemic power over our own bodies, what the fuck? You're trying to apply cisgender dynamics to transgender people. It just doesn't work. That's why these discussions have to take place.
If we can acknowledge and understand that trans women and cis women have different experiences—and that trans women are marginalised by the cispatriarchy in ways that cis women are not—whilst simultaneously understanding that they are both women, why can't we understand and acknowledge that trans men and cis men can belong to very different social classes whilst still being men?
You are not a transgender man. You have not experienced the lived reality of being a transgender man. You are very clearly detached from the material reality of the world transgender men have to navigate, and should not be trying to dictate what does and doesn't benefit us.
"...trans mascs are more likely to enact misogyny [...] because of their relationship to it as a beneficiary"? The effects of misogyny aren't escaped when we transition, they compound, and while outliers will always exist, as a community we certainly do not decide to become misogynists when we transition. That is, genuinely, a TERF argument. Unlearn it.