I don't think she's testing Fuyuki, but there is definitely something off going on. The way she accepted his confession was ... less than enthusiastic and when she asked Fuyuki about getting a boyfriend during the sleepover, it didn't sound like she got the answer she was hoping for.
I'm not entirely sure why she agreed to start dating him, but I feel like she was looking for a reason not to.
I think you're mostly spot on, the way I see it, she's probably in love with Fuyuki but likes Ryou very much (as a friend) and is not really able to sort out these feelings and understand them as what they are. She probably believes that something like a romantic relationship with Fuyuki is unattainable so she's turning towards the other option open to her and since its someone she definitely has a strong connection to and likes, she might think that getting together with him would be the "natural" way for things to develop.
In that scenario, her lukewarm acceptance would make sense, it is not really supported by strong emotions after all, rather just being born out of following what is "normal" and probably also not wanting to reject a person she actually likes (though not in a romantic way). Her interaction with Fuyuki the night before would also fit, she might have some sort of awareness of feeling something for Fuyuki and wants to sound out what her reaction would be and does not see anything there that would make her believe that Fuyuki would even be a romantic option.
So in summary, I also don't think that Eri is "testing" Fuyuki or anything, I think she's just a romantically confused girl in a heteronormative world