This topic was a favorite of one of my Japanese professors, and she was vocal about how she felt the Dictionary of Japanese Grammar misrepresented this grammar point (for reference, she had a PhD in Japanese Linguistics and was a native).
Unfortunately, I can’t regurgitate exactly how she explained it to me because it’s been awhile, but there’re a number of factors at play when using 「そう」「よう」「らしい」and a number of other words in the same “category”.
Are you getting the information directly or indirectly? How much conviction do you have about X? How much of your judgment is based on available information vs. your own thoughts?
「そう」is when the information you’re receiving is direct only, and you have a pretty strong conviction about X. In a scenario (which I’ll link below), you’re looking for a book. Your friend suggests going to some bookstore, and when you arrive, you notice that it’s a fairly large store. You think “With a store this big, it’s bound to have my book!” (「大きな本屋ですね。ここならありそうです」).
Your friend says 「ええ、たいていの本はあるらしいですよ」, as they have no personal experience with the store, but heard information from someone else. Indirect information + no personal connection to/personal conviction about the content of the information they’re sharing.
After browsing the store for a while, you haven’t found the book, so you say 「いろいろ探しましたが、ないようですね」. You’re still using the available (direct) information you have, but your conviction in finding the book has gone down after searching and coming up empty (you believe less strongly that you’ll find it).
Sorry for the wordy explanation (which I’m not sure even helps), but this link and this link might help. The example I used is in the first link, near the bottom, and both links are in Japanese. There’s also this answer.
I also checked some grammar dictionaries I have and they say somewhat similar things, though not as wordy as the first two links.
TL;DR: It’s based on a bunch of stuff and maybe click the links instead of listening to me.