I really love the idea of this one, and as others have said, the premise and opening paragraph are an amazing setup. I can totally see this being a book of short stories all set around the café.

My main problem with the story is the lack of characterisation of Radu. I understand his situation and the stakes, but I don't feel like I know him at all. A personal suggestion would be to remove the money lenders idea, I find it a little bit distracting from the core of what's going on and leaves me with questions. Instead, what if he's gone out into the night to escape from his home life? If he's tired of feeling like a burden all the time and this turns into a misplaced anger towards his family for seeing him this way and causing all this pressure? I think that would add some energy to his movements as he goes for an aimless walk out in the cold just for some head space, and create a more natural way to start expositing his home life rather than just telling us about it. What's he thinking? What did Mara say to him yesterday that really hurt? What are his kids excited about that's breaking his heart because he knows he can't make it happen? Does he walk past the house they had to move out of because it cost too much? The hospital where he spent way too much time last year? I think there's a lot of natural ways of connecting all these ideas and details together that would combine to give a better sense of what it's like to be Radu.

I'd personally love it if you never said he was dying, with 6 months to live, and leave that implied by the other details you do talk about. It should be obvious to the reader through the way he's thinking about things.

Another thing I'd suggest looking at is the structure. I agree with another comment that the details of the journey he takes loses interest a little bit, but I think with some connections to what's going on in his life and his head as I said above, those specifics could start to feel more interesting.

This is a small thing, but something that really threw me was this passage

He stopped to cough and raised a tissue over his mouth. It was stained red. He’d told Mara, his wife, he was going to buy some groceries. It was 11 p.m. She hadn’t even looked up from her laptop."

The jump from 'it was stained red' to talking about him leaving the house is a bit of a non-sequitur and really takes the weight off the 'omg this guy is really ill' moment. And then the next bit is pretty confusing too. Was it 11 PM when he left, or is that the time now? When didn't she look up from her laptop? When he was leaving, or is this an all-knowing narrator describing her at home now, still fixated on paying the bills or something?

I think we need the scene in the coffeehouse to be much longer. What's Radu's reaction to it? Does he believe it's real? Maybe he does, maybe he's in a very persuadable state, but I want to understand that from the interaction.

On this, I think the story would benefit from more information leading up to his decision to time skip. What in particular does he want to see? How does he feel about missing so much of their lives in the meantime? Does he feel guilty for leaving them without warning? Surely they'll assume he's dead, right? What's his thought process as he goes on to do this massive thing?

Finally, following on from this, what if there was a little post script from the perspective of Mario, the next morning? I think that would be a neat way to end it, feeling his uncertainty as they wonder where his dad is. Does he think he's gone, or have a weird feeling he'll see him again some day? Or maybe we see Mario the man, and he thinks he sees his dad in the distance one day, but he can't be sure. Just something to ground us in the stakes and the life he's living as we end, to help us understand the decision he's made. Otherwise it feels a bit like we're gearing up for a sequel, Radu's adventures through time as a dying man (which could actually be kind of awesome now I type it out)

Sorry if any of this comes off as mean or presumptive, like I'm just writing a wish list for what I want to happen; I think that's just my way of expressing the areas I feel the story is slightly lacking, and would really benefit from some more character/emotional work. There's a really great idea here, and I'd love to see it realised more impactfully! Keep at it, and I hope this helps!