Rougo ni Sonaete Isekai de 8-manmai no Kinka wo Tamemasu
Saving 80,000 Gold in Another World for my Retirement

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Manga in which the premise includes the free movement between our world and another, but also manga about returnees or other similar situations that transcend the barrier between worlds.

Manga that fall under the fantasy genre that use that genre very generically
these are usually light novel adaptions

Isekai Mangas/Manhwas in which the main character has the ability to freely travel between the real world and the Isekai world.

If there any any others that you think belong here, feel free to message me.

Since I've had trouble finding it myself, here's the collection of manga where the main character(s) have the advantage over the Sword and Sorcery world by flexing the most powerful magic of all: GUN.

Not saying they're all good, but I just want to collect as many in one place as I can.

Not on MAL:
Queen Cesia's Shorts

Webnovels with similar concept:
A Budding Scientist in a Fantasy World [RoyalRoad]
A Chemist's Rise in Another World [RoyalRoad]