It doesn't need anything. You may need to remove the shroud to service it, so you really should not seal it to anything with something like caulk. You are not up on a ladder viewing it anyway. It's fine.

No wouldn’t caulk it - just don’t like the gaps. I’m tall so I see it every time I walk by.

Those are really minor but you notice it because it's new.  I bet that a year from now,  it won't bother you.  I also don't think anyone else would notice it.

Know what bugs ME about that chimney? The horizontal seam that accentuates that it's a one-size-fits-all chimney with an adjustable height. That won't bother most folks! But it just shows that different things bother different people.

One solution would be a custom made chimney shroud. But it's probably not really worth it.

You can caulk it if you think it will help. Caulking doesn't make things inaccessible. It just means you'll have to remove and replace the caulk if you need to get in there. Caulk isn't JB Weld! It peels off and is easily reapplied. It's not supposed to be permanent.

How often have you serviced a hood in the past, anyway?

But really, it's not terrible. There is no reason to NOT have a crack there. Things aren't meant to be seamless!

The horizontal seam isn’t great either honestly. I would much prefer one seamless shroud but not worth the cost. Def don’t think grout is the answer but I don’t think ignoring will work for me either. Will see.

After building a house and having lots of little things bug me, I can assure you within 2-3 weeks of using the kitchen daily, you won't even notice anymore. And I say that as an artist who used to teach workshops where my students called me Eagle Eyes.