It's not just permitting speech the left doesn't like. I don't care enough to follow this closely and have a bunch of sources at the ready, but it seems that left leaning accounts which do not violate the rules are being targeted by twitter in various ways. There was a pro-palestine account which people said they would follow and then go back and somehow see they were not following it. And some words can imply violence - for example doxxing is "just words" but presents real world risks to people, and there are other forms of harassment which are seemingly against twitter rules which is being permitted. Famously the libsoftiktok account posts a lot of harassment of trans people, and internal leakers at twitter show that this account has been flagged to prevent it from being banned even when it violates community standards.
So actual rule violating accounts are purportedly being protected, while left leaning accounts which do not violate rules are being manipulated behind the scenes, if the reports are to be believed.
Again I recognize that I have not provided sources and I don't expect you to just take me at my word, but I wanted to correct what you think I am saying. I am not just concerned with uncomfortable speech, but outright harassment and the apparent suppression of certain left leaning accounts. That is why I say it is about controlling the narrative.
EDIT:
Did a couple of quick searches. Banning journalists for being critical of Musk/Twitter isn't very free speech oriented!
December 2022
https://www.pbs.org/newshour/nation/journalists-who-wrote-ab...
April 2023
https://www.vanityfair.com/news/2023/04/elon-musk-twitter-st...