" How do I fix that to look nice and sturdy? "

Are the two floors the same height? What was there? How much clearance is there under the door? How thick is your LVP flooring? What are you going to do with the current oak transition strip?

So originally there was a carpet there which I pulled out.

As you can see the carpet was on top of that patch. There is some height difference between the lvp and the oak floor now with that broad patch in between.

" There is some height difference between the lvp and the oak floor now with that broad patch in between. "

Which is lower? How much height difference? Take out the oak transition piece and have one wider piece of oak milled to sit flat. The balance of my previous questions are also pertinent.

Are the two floors the same height? They are now almost the same height, maybe a 1-2 mm difference but not much.

What was there? The rug from the latest comment picture

How much clearance is there under the door? Door has some clearance even with the oak transition, we use something to block cold air in winter, I think about 3-4 mm atleast.

How thick is your LVP flooring? 4mm.

What are you going to do with the current oak transition strip? I hadn't thought about it, hence the question. I can remove it to do what you suggest here i.e. adding a wider one.

Remove the gold metal trim. Keep flooring until you get to the oak floor and install a T-molding or reducer.

" Remove the gold metal trim. Keep flooring until you get to the oak floor and install a T-molding or reducer. "

That would work perfectly as well. It actually helps that the floors are almost level.

thank you so much to @millworkman and @G & S Floor Service, that makes sense to add another lvp till there and then add the T-molding.