@Podi125 to add, and correct a bit of what you said:
Rakan never knew she was pregnant. He didn't even suspect it in the slightest., nor did he ever think of the possibility of her becoming pregnant. The reason for this is stated
a few chapters back. Courtesans frequently take contraceptives, and in the unlikely event that they do get pregnant, they abort the child. The only possibility for a child to be born is if the mother wanted it to be born. The problem that occurred here was the lack of communication and the unfortunate timing. Fon Shen wanted to be bought by Rakan, but she knew Rakan didn't have the money, so she thought of lowering her price by becoming pregnant. Keep in mind she never told this to Rakan. Rakan was already trying to buy her before this by begging his family to buy her, but they refused since they didn't want a courtesan to be the main wife of someone in the family. Then came the part where Rakan is sent off, and the only method of communication between the brothel and Rakan is through letters. The problem here is that the brothel did not know where Rakan went (they knew he was sent off to somewhere since he sent them a letter, but they did not know where he was). So, the only way of contacting him was through the family, which was opposed to Fon Shen becoming Rakan's wife. Once Fon Shen was known to be pregnant, the brothel urged Rakan to come redeem her, or at least have someone redeem her in his stead, but once again, the family. They did not forward the letters to Rakan, so he never knew she was pregnant until he came back and saw those letters. During the entire time he was gone, everyone at the brothel eventually begun to suspect he turned tail, so once he came back after all those years, they naturally did not trust him and lied about Fon Shen and the child.
Christ was is this entire situation fucked, like, if just one thing went differently, the entire tragedy could have been avoided, yet... ugh.
This is what I can remember from the web novel, the setting should be roughly the same here, but this manga avoids explicitly telling the reader everything. The web novel is much more direct when it comes to telling its readers what's going on. I'm not too sure, but I think the alternative setting manga is also more direct with its story telling, so when it reaches this point, it might explain it more than this manga did. But we'll have to see.
Also tagging you
@Otaku713 if you're interested.