"I'll look after you" is not the same as saying that she'll give you some of the inheritance. I'd say that means that if you had a issue she's there to help, not she's going to give you money.
And it seems odd to have discussed it so much. I mean, I don't think I'd have expected it to have come up in conversation much. I'd agree with the person who says if the Op brought it up, then it's grabby, if the sister did, it's braggy.
I had lots of great aunts and great uncles. I don't think any sent us cards at birthdays. I do know that one great aunt had a soft spot for dsis. Entirely down to having a joint interest in common.
But the dsis had a relationship with him. Presumably she's now mourning, which the OP clearly isn't. People do feel differently at this point than when it's a theoretical possibility.
Maybe she thinks that it's a nice momentum of her Great-Uncle that she went out for lunch with, to take her family out to lunch. Maybe the will says "I give it to Op's dsis on the basis she gives none to Op because the only time OP came to see me, she spent the entire time talking about how she deserved 50% of the inheritance". Maybe the dsis knows her/her dh is about to lose their job. Maybe someone else has come forwards and said "if you're giving some to Op, I deserve some too..."
We can't know any of this.
The only thing we can know is that the money has been left to the sister, and it's for the sister to choose what she does with it.