2024: Han Kang -- no LGBT themes, characters, or plots
2023: Jon Fosse -- no LGBT themes, characters, or plots
2022: Annie Ernaux -- no LGBT themes, characters, or plots
2021: Abdulrazak Gurnah -- there are homoerotic themes in some of his work but the characters are not gay in terms of their identities, and homoeroticism has more to do with the ideas of power rather than sexual identities
2020: Louise Gluck -- no LGBT themes, characters, or plots
2019: Peter Handke -- no LGBT themes, characters, or plots
2018: Olga Tokarczuk -- I think her work is the one that fits your description best
2017: Kazuo Ishiguro -- no LGBT themes explicitely AFAIK, but queer readings of his work are a thing
2016: Bob Dylan -- no LGBT themes, characters, or plots
Gurnah is an immigrant (a refugee to be more precise) who can be considered living "in a diaspora" and his work does focus on the topic prominently. Ishiguro is a British citizen who thinks of himself as British, I believe, his parents moved when he was very young IIRC. He didn't visit Japan until his adulthood. I don't think his works are "disapora-adjecent" thematically but I only read two of his novels, so not completely confident here.
The rest write in their native languages and live in their birth countries.
I believe when you mention Carson's LGBT text, you refer to Autobiography of Red, it was written in the late 90s, not this year.
Edit: fixing typos, punctuation, and wording