Can try to look up something maybe they don't release it anymore. Last time I saw it it would be a september if I rember correctly, and she wasn't doing nearly half as well as you would suspect given all the controversy that was going on back then. Hell Gale of all people was ahead of her and by much so once again - she isn't nearly as popular as you claim her to be
There are no September stats. You're conflating that with the August stats where Gale is in fact ahead of her. I don't think it was surprising that he was the default pick for most players, given the player demographic. But Karlach coming in second, beating out everyone other than Gale, is a very strong testament to her appeal.
I work in a media analysis company. Social media trends are part of what we track for a living, and it's how I know Karlach is very popular to this day.
What Larian showed in their August data was that Karlach was immensely popular out of the gate. I doubt that trend has changed much, given Karlach's sustained popularity on all social media platforms.
Karlach's strongest platforms are YouTube and Twitter (I hear Tumblr as well, but I can't confirm that). Her cutscenes on YouTube have massive viewership, beating
everyone else including fan favorites Astarion and Shadowheart. She is repeatedly the most requested character for fanmade content on that platform, too, having two songs produced by popular YouTube musicians (and a third one on the way). She was prominently featured in Larian's first promotional animation after the game's release. That's not an accident.
As for Twitter, fan content shows what people are excited about. Fanart is perhaps the most important metric in that regard. There's an old meme about how Overwatch's popularity is sustained by its Rule 34 content, and there's a lot of truth to that. You can draw a direct line between how popular a character or a game is and how much fan content is being made for that character or that game as a whole. If a given character consistently gets a lot of fan content that is highly liked, that shows you who the most engaged players gravitate towards.
On Reddit, Astarion and Shadowheart are unquestioningly the most popular. Lae'zel also had a very strong presence up until recently, but Karlach content is consistently seeing posts with thousands of upvotes. I haven't checked recently to see if their spots may have reversed.
I won't bring up the Discord thread, or this one, because they're a different kind of data point.
Lastly, two of the three patches have been Karlach-themed. You can chalk that up to August's excitement. However, Karlach is still the most featured character even in Patch 3.
All of these are things you can check for yourself using the corresponding search functions. You don't need to take my word for it.