Do anime, videogames, and other media have effect on the recent trans boom we've seen over the past 5 years?

No and yes
We have always had traps and androgynous characters in anime since ages past
Maybe the reason we didn't see many people dress up as anime traps before was because anime wasn't mainstream or because there weren't too many
But not today
Nowdays anime traps are not only extremely popular but they are to be found in great numbers everywhere, with some of them extremely popular characters from famous series (Astolfo, Felix) which in turn increases the amount of "Cute Trap" fame around the internet
Which in turn leads to impressionable young men wanting to "be the gf" or "be a cute girl (male)", a clear case of Reality attempting to replicate Fantasy, but taken too seriously and inevitably leading to ruin and dissapointment
TL;DR: Kids have always been impressionable and aspire to be characters they like on their TV series, same deal with teenagers at 15
Except Normie media incetivises this fantasious behavior confusing it for acceptance of Transgender culture on mainstream world
I mean, c'mon, cosplayers do it much better and they're not confused teenagers, why not follow example?

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Partially this, OP.
What the other user misses is that BECAUSE Trans people are getting more of a voice, they aren't being forced into porn *as much (Something, I personally am grateful for).
Wider social acceptance has led to both, a lot of trans people being able to realize "Oh, THAT'S what that is," and given more reasons to the families and friends of trans people to think, "wait, there's no reason to excommunicate this person," - this results in not needing to appeal to coombrains to transition, as with friends and family there's access to emotional comfort and possible financial support [depending on age].
Though as said, there is no "Trans Boon," at least in actual amount of Trans people - just a "Trans Boost," of representation in Media.
Is this a bad or good thing? Eh... There's pros and cons - though it should be explicitly stated, those pros and cons are towards the Trans Community. There isn't any "DANGER" about trans people being vocal towards anybody except trans people.

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>people are born gay delusion 2.0

Kind of?
Anime is more Japanese Culture Centric, which Japanese Culture prioritizes male sexuality to a greater degree than female sexuality.
It's why Traps and Gay/Bi Men are "Kinky" and "Hot," but Lesbians [and attraction to Lesbians in a Sexual context] are seen as "Degenerate," and Trans-Men a "Joke" or "Disgusting".
>The Penis Makes it Cuter/Okay
Is not a Meme in Japan.

>people are born gay delusion
>STILL believing this (((lie)))
We are social creatures above all else user, some of us are born Gay to prevent conflict in the tribe. Some of us Bi. It's an active benefit if people don't sperg out about it without recognizing the benefits.

I don't know maybe

Yuri exists
Existed before traps too

No, thank Obama.

This isn't an issue of "existing before" but "being ostracized".
It is seen as "more degenerate" in Japan to like Lesbian porn or be a Lesbian [or a Bi woman] - than being Gay, or Bi [as a male]; there is a couple outside perspectives as to why, but, the internal one seems to be that "women being queer" is interpreted as a loss to the collective society [i.e. B-BUH DA EMPTY WOMB], something that is a consequence to the very real appeal to conservative roles in relationships that Japan takes [IFF people decide to date].

Yuri is considered something Japanese girls grow out of, unlike male experimentation

Aye.

that's a boy

So, how does being trans fit in? How is someone having unbearable mental anguish that can only be alleviated, to some degree, with hormone pills benefiting the tribe?

It's not just mental anguish?
Like, I understand personal experiences are trash data-wise, but my parents fucked me up enough that I had already developed healthy understandings of the self, and of my body, that by the time I realized I was trans, I could mitigate the ""anguish"" into "discomfort".
That being said; [in the case of MTF] Orphans; you're dealing with an individual who doesn't want to procreate for deeply uncomfortable reasons, yet still deeply wants to care for children.
You're basically given a Caregiver, who isn't inhabited every month, who goes the extra mile to because there's an explicit want to fill the role, and who despite even the most extreme anguish - is just trying to insure the preservation of the Kin, not the self.
In this aspect, it's more spiritual.
Medical advancement to let these people transition is a byproduct of where we are; but, looking at the history of Native Americans, Trans people have been here; and, seeing them as trans isn't a medical advancement but an acceptance that we're not simple creatures.

I must admit I'm among the people who don't get the concept of gender, but I'm willing to - in the words of Bill Graner - believe in what works for people.
However, adult biological males believing that they can look like women, setting them up for constant failure and social rejection in the thing they are most sensitive (or obsessive) about, gives me the idea that transgenderism FtM is not working.