I'm really struggling to find the war being waged on trans people here -
https://www.bbc.co.uk/search?q=transThere are numerous programmes on the lives of trans people covering a variety of topics (relationships, culture, health), some news stories reporting facts (mainly people and organisations getting 'cancelled' for being anti-trans) and articles based on public comments from well known people regretting decisions.
I assume you are referring to the controversy around a single article by a single journalist [1]. A journalist who previously wrote a sympathetic history of trans people in the modelling industry... for the BBC[2].
Out of curiosity, I tried to find any other evidence. All other descriptions of this anti-trans agenda ultimately just reference this single article e.g. [3]. One 'article' becomes 'articles' and then slips into being an 'agenda'[4]. I found one other reference - an article about an internal meeting which some attendees complained about, but that wasn't even public facing and was only called because of that single article [5]. (There were also some vague references to two individual news stories, which were considered by some to not be balanced - there are complaints like this about news coverage from either side of any argument every single week on the programme Feedback.)
If the BBC is trying to promote an anti-trans agenda across their massive output involving tens of thousands of people, they are doing a spectacularly bad job of it.
I get fed up of people bashing the BBC over individual incidents - it just feeds into the right wing narrative that it needs to be de-funded [6]. Be careful what you wish for, privately owned media tends not to be great for marginalised groups...
[1] https://www.bbc.com/news/entertainment-arts-59074096
[2] https://www.bbc.com/news/uk-england-49578690
[3] http://www.ilga-europe.org/sites/default/files/2022/united_k...
[4] https://www.gaytimes.co.uk/life/drag-race-uks-bimini-calls-o...
[5] https://www.pinknews.co.uk/2021/11/11/bbc-trans-lgbt-staff-s...
[6] https://www.gaystarnews.com/article/mps-and-trans-campaigner...