I become a full member of Thieves Underground after I delivered the map to sewers to Thaddeus Mynor. The first rumor (job) was about Cedric Appleby wanting something to be stolen from Bates, but Cedric hates me because I already finished the ring quest in favor of Bates (no sabotaging).

Do you know if there is any legal way to force him to speak to me about business?

No, it doesn't change anything. He repeats the same line over and over again.

Nevermind, according to GameFAQ there is no point in that:
"He might also mention that Cedric Appleby is looking for a thief to steal something from Gilbert Bates, but that’s just the evil method for finding out about the Black Mountain Clan. (And, if you’ve already helped Gates, Appleby won’t talk to you any more anyway.)"
https://gamefaqs.gamespot.com/pc/914155-arcanum-of-steamworks-and-magick-obscura/faqs/13910

I guess that makes sense. Unless you're sold on doing all the quests in the Thieves Guild (and have already talked to Bates all the way through to the end, on a previous playthrough) revisiting Bates and keeping him updated throughout is the more rewarding option, both financially and in terms of backstory.

Also, thanks as well for that link.

I know I'm late on this one but that journal entry is not a Thieves Underground job.
It's a local rumor, just like these ones : https://i.ibb.co/Y7pPT1F/Rumors.png

This is how a Thieves Underground job looks like : https://i.ibb.co/fQywRN8/Thieves.png