there is "I Won 4 Billion in a Lottery But I Went to Another World", which is half of what you want.
it has an adult protagonist, without any litrpg stuff.
but It's a light hearted romcom story, rather than a bloody action thing, and as far as I read, the existence of the Gate isn't publicly exposed yet.
the story is that our average japansese man wins the lottery, and runs off to his grandparents house in the rural area to avoid people who want the money he won. in the basement of the house there is an entrance to another world, where he encounters a struggling village (and a pretty girl), and decides to help them by bringing in supplies from modern japan. it then proceeds to have him involved in the fantasy politics, par for the course. with a few girls added as the story progresses.
there are some weird overtones of Japanese excellency in how food from japan is inherently better, and maybe some fetishization of manufacturing (which is kind of normal in these stories). but as long as you don't expect it to be something it isn't, then it's ok.
I quit somewhere after 20 chapters, mainly because I couldn't stand the hypocrisy of using his "un-earned" money to help the village (by buying a few thousands dollars worth of fertilizer, or spending 50K on a terrain vehicle to transport them) and this being treated as a moral action, while clearly condemning the people who wanted him to use his money to help real people on real japan, with real problems which require real solutions, which won't result of him being treated as a savior.