Is he shy or just being polite (i. e. not interested)?

Please be kind:

29f here. I met a guy at evening singing classes who seemed nice but very reserved. He barely spoke to anyone except the tutor. In the first class, I noticed him staring at me once, and after that he occasionally glanced at me, usually when he thought I wasn't looking.

We seemed to have similar tastes in music (basically making him a unicorn), so after the first class I somehow worked up the courage to ask for his number, ostensibly for a group chat. A couple of days later I messaged him directly about the class. He replied promptly and thoughtfully, but didn't respond to my last text, so I left it there. I'm currently tackling lifelong social anxiety, so I'm probably a bit rusty/ too familiar.

A few weeks later, our tutor paired us for an improv. I lightly teased him, and he laughed, smiled broadly, and looked down at his notes. After another class, he seemed to linger, so I asked gently if it was ok to walk to the station together. He said yes, but was extremely quiet. Hardly any eye contact, arms folded, long pauses before answering, and he rarely elaborated or asked me anything in return. Convo was hard to sustain.

I wondered if he wanted to keep things formal or had a girlfriend. Before he boarded his train, he did ask whether I'd be at the final class. I said yes. By then though I assumed he wasn't interested and didn't want to make him uncomfortable, so after the final class I left alone.

Then, the next day, he texted me outside the group chat: "Hey (name), meant to catch you after class (he'd never approached me before) to say your song sounded great! Hope you are well". I'd noticed him listening during my performance and nodding along. I replied warmly, thanked him and said I hoped he was well too. That was a couple of weeks ago, and nothing since. Am I imagining things? Was he simply awkward, or polite?

Shy-guy input especially welcome: should I follow up, or leave it since I've already initiated twice? I don't want to come across as weird.

Is he shy or just being polite (i. e. not interested)?
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