As someone who read a wide variety of high fantasy novels over the years and experienced the golden age of fantasy (1980-2000) novels in the US, I am a lover of adventurer stories.  This doesn't change even with switching to Japanese web novels, where 'true' adventurer stories are a solid minority of the isekai and fantasy genres.  

First, for those who are unfamiliar with the difference between isekai and high fantasy, it is fairly simple.  Isekai requires that the protagonist have an origin in one world and be present during the story in another, so it doesn't strictly require the story to be pure fantasy (science-fantasy and certain types of science fiction also work).  High fantasy, on the other hand, has no involvement with our own world, often having various rules and powers such as magic or psionics that don't exist here.  

A 'true' adventurer story - as I define it anyway - is a story where a protagonist becomes an adventurer and travels the world, builds a life as an adventurer, and/or delves dungeons for profit and exploration reasons.  However, there is also one last requirement... the protagonist can't be 'overpowered'.  The hardships of the story are part of it in general, and an overpowered protagonist - by nature - isn't adventuring, he is vacationing, lol.

Not that I don't love overpowered protagonists in isekai and fantasy settings, but for someone who wants to vicariously experience adventures, overpowering the main characters generally isn't a great idea.  If the protagonist is overpowered, then his enemies need to be overpowered as well to make the story a true adventurer, and these days, most stories of this sort in Japan tend to nerf the antagonists in general.

Annainin wa Isekai no Jukai o Samayou

https://kakuyomu.jp/works/1177354054918935123

This particular one is the one I think of the most when I think of 'True Adventurer Stories'.  The protagonist of the story gets thrown into an isekai by a random portal and has to struggle to survive in a forest before eventually reaching civilization.  He eventually manages to return to Earth, where he ends up becoming a guide for people who want to pass through 'his' portal to the other world.  It is a very down to earth story, with a protagonist who is capable but not overpowered.  

Isekai Ten'i, Jirai Tsuki

https://ncode.syosetu.com/n0350em/

This is one of my more recent favorites, as I only finished it up to its current end point a few weeks ago.  The protagonist of this story dies - along with his entire class - and gets the option to select skills using points gained based on his capabilities and talents on Earth.  As other members of the class request powerful 'cheat' abilities, the evil god (self-proclaimed) tells them there is no such thing as a cheat ability, and he learns when he selects 'Help' as his first skill selection that all the classic cheat skills (Skill Theft, Skill Copy, XP increase, etc) all have massive demerits that far outweigh their benefits.  Thus, he avoids the traps and selects a skillset based on surviving in the new world, where he is joined by his childhood friends Touya and Haruka.  The early part of the story is them starting out as adventurers and building a life base for themselves in the town they arrived near, while slowly raising their rank and improving themselves through training and fighting monsters.  While the protagonist and friends are pretty capable by the end, they are - at best - on the higher end of the average veteran adventurers in capabilities, so you won't see them overpowering everything from the front like a lot of isekai protagonists.

Bastard Swordsman

https://ncode.syosetu.com/n9619hu/

This one follows a reincarnated protagonist who was born between two people of different ethnic backgrounds (and is thus a target for mild racism) and works as a low-ranking adventurer in town.  While he is technically overpowered, he almost never shows this in his regular life, instead mostly working odd jobs and helping out those around him.  If he doesn't use his special ability (which is basically a trump card that takes a lot out of him) he is about as strong as the higher-ranking adventurers, but he deliberately spends his life taking on small jobs, occasionally dribbling knowledge from his previous life anonymously to those who can use it, and generally just enjoying life in general.  This is pretty much a slow-life story, so don't expect anything grand out of him.

The fact that I can only name three such web novels, despite devouring tons of fantasy and isekai over the past five years should tell you just how rare this kind of thing is.  If any of you have any suggestions to add to this list, I would be grateful, lol.