I am a caryl shipper, however, I do think the ‘it’s not like that’ scene can be interpreted two ways and that it was intentional.
1) Daryl said it’s not like that and he could actually think Connie doesn’t like him back, so they are just friends. They could have had him say “I don’t like her like that” but that would be too final
2) they had the “we’re family” scene an episode before to make Daryl question things
3) they purposely had Daryl sigh and look down when Carol first asks about her, kinda like he’s blushing
4) in that same scene, Carol is also being untruthful to Daryl and hiding things from him
5) also, Daryl having a love interest is meant to be a surprise to the audience. They wouldn’t have him admit how he feels so early; it would ruin canon. Think Richonne.
These are the things that have me unsure and I think they need to be addressed. I’m sure tptb will forget about it anyway.
Yes, anyone can interpret it however they please. But in response to what you just laid out:
1) If we're getting granular about the language, Carol's response could have been way more open than "why not?" For example, "You sure?" Then Daryl's silence would have clued us in that in fact, he's not sure. But the line is what it is because we're not meant to question whether it really is or is not "like that." We're meant to realize there is a specific reason why it's "not like that." It can't be because he has no experience in romance since apparently he does. It can't be that he's just too embarrassed to talk to Carol about it because apparently he already talked to her about Leah. Clearly, Carol suspects the reason is that Daryl is still hung up on Leah but, IMO at least, this contradicts Daryl's attitude all throughout S10 where we see him actively building a future, not dwelling on the past. It's only when he's put back in the environment that housed all of his pain that he stirs up past emotions.
Yes, "It's not like that" is a very common trope that often carries the opposite subtext, but there has to be instances beforehand that clue us into that. Whereas in Daryl's case, a moment in the prior episode actually solidifies it's the truth. Which brings me to...
2) Referring to someone who you're romantically interested in (as opposed to already being in an established relationship with) as family is extremely odd. Connie and Daryl are not established nor do they even have the longevity that Carol and Daryl have to create a husband/wife dynamic. So when Connie says she and Daryl are family (not that they belong to the same family, she pointed to Daryl and herself to indicate she's talking about the two of them), it is because she thinks of their relationship as familial. Daryl's reaction was not one of disappointment, but of uncertainty. He wants to feel like they're family, but she hasn't given him a reason to believe it. She just got done devising a plan to lie to the community in order to protect Kelly and Magna, suggesting that her loyalty is with them. We've seen Daryl work hard to make them feel included like Rick and Hershel would have wanted (he fucking learned sign language), and then they go and alienate themselves, so no wonder he's not feeling so great about the family comment.
3) I didn't see a blush. I saw mild annoyance that Carol was bringing up something that makes him uncomfortable (love life in general, not Connie specifically), and worse, something that she had misinterpreted.
4) Daryl knows Carol's been untruthful with him. He's not using it as an invitation to be just as untruthful. Again, Daryl only lies when he thinks he's protecting her. You could interpret his earlier line "The King sends his best" as an attempt to do just that if he suspects Carol might get hurt by Ezekiel's rejection, or (and I think I swing this way), you can chalk it up to Daryl's usual sarcasm when it comes to Ezekiel.
5) The writing has not been nearly as subtle about the potential (key word) for a romantic relationship between Daryl and Connie because that is the whole point. We're meant to wonder about it, maybe anticipate it, and for some of us, fear it. There are much stronger clues that inform us we will never actually see it happen because it's not what Daryl and Connie actually want. Ever wonder why they stopped having private "shippy" moments after the solidifying "you and me are family" scene? Not because Daryl believes he misread the situation. All of it was only needed to earn the scene where Carol asks him about it. From that point on, anything "shippy" is through Carol's perspective in order to tee up her guilt for getting Connie trapped in the cave, which only had to happen because LR went off to film The Eternals.
Hopefully all of this helps you. If it doesn't, oh well. Not much else I can say. You'll just have to be pleasantly surprised when Caryl happens instead :)