Yoichi __ Isagi†

If we're talking about Isagi as a boyfriend, he'd probably be quite different from how he is during matches.
He would be attentive and observant. He would notice small details about you, like your likes and dislikes, things that bother you, or when you're having a bad day. He wouldn't necessarily be super cheesy all the time, but he would show affection through his actions.
He might also be a little shy at first with displays of affection. He could get flustered if you say something too romantic and would probably try to act normal while inside he's processing absolutely everything.
He would be very encouraging with your goals. If you have something you want to achieve, he would try to help and motivate you, because he fully understands how important it is to want to improve. That said, he would probably turn everything into a minor competition without realizing it.
And he'd have a rather protective side, though not excessively so. If someone treated you badly, he'd definitely get serious and take your side. In short: Isagi as a boyfriend would be attentive, intelligent, somewhat shy, competitive, loyal, and affectionate in a way that was more gentle than cloying.

If Isagi were jealous as a boyfriend, he'd probably try to hide it at first. He'd observe the situation, trying to understand what's happening instead of reacting impulsively. Very Isagi: tactical analysis even for jealousy, because apparently romance also needs a map of the field.
When someone flirts with you, they'll probably get more serious and competitive. They won't necessarily make a scene, but they'll try to get closer to you and make it clear they're interested. Then they might casually ask you who that person was, trying to sound casual while clearly NOT being casual.
He might also have a slightly possessive side, but without trying to control you. If he notices someone trying too hard to get your attention, he'd probably think something like, "Why is he so interested in her?" and start observing everything with his characteristic analytical eye.
And if you notice and tease him with, "Are you jealous?", he'll probably get flustered and try to deny it: "I'm not jealous... I was just paying attention." Blatant lie.

Isagi Yoichi is a very intelligent, strategic, and observant player. He has excellent field vision, allowing him to analyze the movements of his teammates and opponents and find spaces to attack. He also excels at anticipating plays.
He is a competitive, ambitious, and determined person. Although he may initially seem calm and somewhat insecure, when he plays he demonstrates great confidence and a desire to improve. He doesn't like to stagnate and is always looking for ways to get better.
One of his most important characteristics is his adaptability. Isagi learns from his mistakes, analyzes other players, and uses their skills to develop his own. His evolution during Blue Lock is largely based on learning, adapting, and finding new ways to leverage his strengths.
He also has a rather intense and selfish side during matches. He's willing to take on strong players and seize any opportunity to score. His "devour" mentality, which prioritizes the skills of other players, is a fundamental part of his style.