I made an audible gasp for that last panel.
I don't... What?!
My guess is that Marten knows that nothing would ever happen if he just sat around and didn't do anything, and he has been getting better at taking charge of his life lately. Now the question is how Claire will respond to this. Martens feelings seem pretty clear, I doubt he'd do any of this just to tell her "We can't date/I don't want to date you"
in that case he's an oblivious asshole. But to be faire, he seems happy to be there. Almost drunk...
... with love?
I'm not sure he's drunk, I think he's just happy. He knows Claire is a genuinely good person, he knows he enjoys her company, and he knows that there is a mutual attraction there. There's not a bunch of emotional baggage/tension like with Faye or Dora, and the relationship didn't immediately escalate to physicality like with Padma. His other relationships (or near-relationships) all started rather abruptly, with very little warning. This is the first relationship Marten's had that started as a friendship and gradually and naturally grew into something more. However, it's not like Marten has spent weeks or months mooning after her or is agonizing over how to proceed with things. He's had time to think about the possibility and approach the situation on his own terms.
So from my perspective, Marten is just happy. He knows he is not at risk emotionally for two reasons: Claire is clearly attracted to him, so the risk of being turned down is unlikely if he doesn't rush things and freak her out. Also, while Marten is clearly attracted to Claire, it doesn't seem to be a "I LOVE YOUUUUUUU PLEASE BE WITH ME" attraction a la Sven with Faye. He knows he would be happy in a relationship, but it seems to me that
he would still be happy while not in a relationship, so he doesn't feel the pressure to "get" someone. He also knows that Claire is definitely at risk emotionally right now, and as her friend he wants her to be happy. So he's making his advances politely and openly, trying to make sure there's as little risk of causing a Claire freakout as possible.
I agree though, old Marten would never have handled it like this. That may be why you thought he's acting like he would if he were drunk.
Sorry for the wall of text.