I have seen this in one or two animes (plural of anime?) where characters have long cylindrical protruding mouths. It is quite rare(?) as I had seen this in only a handful of anime shows (I don't know the names). The recent ones that I know is Haganezuka and Kozo Kanamori from Demon Slayer (the blacksmiths/sword makers who made swords for Tanjiro and Inosuke).
The other one that I remember is a fishmonger in Ninja Hattori (a show (is it an anime?) I used to watch in my childhood days) and it is always the fishmongers and shopkeepers. I don't remember any main characters or any characters noteworthy. First of all, that feature is not possible biologically/in real life. So, why is it adopted in anime and cartoon shows? What is it called (if it is a trope)? What is the origin of this feature? Are there any characters noteworthy having this weird facial feature/wears this mask?
I found this picture after a little bit more searching:
It said "O-face (octopus like face)". Searching for "octopus like face" yielded me no results. I do know about O-face which is ahegao (NSFW). But I don't think this applies here.
It is not the pout face or the side faced lips expression (I don't know the exact name either(?)). Below is Suneo from Doraemon.