I think their misreading is understandable because this story's connection with harem is a little complicated.
- It's not a harem because the affection from secondary characters is within non-romantic bounds for single-romance, non-romantic, and real life contexts. There's not even third-party pining. Case closed. Literally not harem.
- The story satirizes harem. That includes friendly affection, which alludes to the original timeline and rivals. Teasing about romance and rivals will be misread as harem. Teasing a harem is a fairly reliable heuristic for recognizing harem, and this meta-about-harems story trips the heuristic.
- An episodic cycle of characters approving of and even flirting with a protagonist is common outside harem, where it's almost universal. This builds up the protagonist's self-esteem and apparent worth. Suzuna notes this, and is living evidence the trope overly idealistic, because she needs one close ally above friendships.
The story and Suzuna's troubles are only one degree removed from harem by satirizing it, so it will be extremely hard to convince people their yuri/shipper goggles are on too tight until well past the halfway point. Especially if their heuristic or personal definition is satisfied by the bevy of tropes common for harem stories.
