As someone already mentioned Mushishi; Natsume Yuujinchou is just so soft! I don't know how else to explain it.
I am old, so 2000s Fruits Basket, as well, mostly, as I actually finished it. I'm really attached to Ritsuko Okazaki's score. I haven't finished the recent series, but the 7 or so eps I've seen, made me super happy, as I wanted a series that adapted the full manga, and it nailed a lot of what I remembered.
OK, one more, as rereading your post reminded me of another romance series: Wotakoi! Sadly a short anime, but the manga has good feels, too.
Hey I remember a Hank Green video about this. I suffer from time to time with not being able to burp either, so I tried to remember this. Basically, botox injections are found to help for not burping, I think a specific variety, where a muscle is not working right. I think it's more in the testing phase, but maybe, you too could burp someday!