Rainbows really don't need any extra colors or symbols. The whole point was that they're already covering the whole spectrum. Giving everyone an extra color completely defeats the purpose and singles out all those who aren't having their unique color added to it.
Then I'm sure you're also familiar with the ransacking of Hirschfeld's Institute for Sexology in 1933, where some of the first treatment plans for trans people were developed. It was a place where gay people and trans people were accepted and treated with respect by medical personnel.
That famous picture of the book burnings? Those were patient records and the research archives of the institute. So no, it did not just start with gay people, and trans people's persecution by nazis was relevant to bring up because it's one of the first kinds of persecution the nazis did. Dismissing that is ahistorical and dismissive of the history of oppression of trans people.
The base flag is always just the rainbow. The other additions are meant to highlight whatever needs highlighting. In LGBTQA+ contexts, you can add the trans and poc and whatnot because those are marginalised groups that deserve some extra visibility.
yeah, its to the point where when I see a rainbow flag I automatically go "This is not for me, this person is not safe"
Same with the still prelavent "Love is love" slogans. That's great, but I'm aroace and trans so uhhh? Guess I'm not included. Better be safe than deal with a transphobe (and be sorry)