Dear Esther, What Remains of Edith Finch, The Vanishing of Ethan Carter, The Suicide of Rachel Foster, What Never Was, Tacoma, Firewatch, Draugen, Martha is Dead, Everybody's Gone to the Rapture.

What Remains of Edith Finch, Tacoma and Everybody's Gone to the Rapture would probably be my pick of the bunch.

Hi Higgles OG(tm) ..."like" is very much you asking other people what they thought the game was like first, then asking threm to give you suggestions based on their takes not yours? What aspects of the game you are really looking for, the graphics style, as in perhaps Scanner Sombre or Life Is Strange maybe, or the strong story, that might run to What Remains of Edith Fitch,Suicide of Rachel Foster, or the game mechanics of The Painscreek Killings or maybe the game mood for Everyone Has Gone to the Rapture or perhaps to push to the depths of Dear Esther or the extreme of Trauma perhaps? Here is a thread is not that old in the grand scheme of things, might be a place to look more broadly:
https://gtm.steamproxy.vip/app/232430/discussions/0/3546050190332439016/

Or since Gone Home is on sale right now, were you looking for some free games? https://store.steampowered.com/curator/41773079-EmpathyGames/list/93017
Or were you looking for emotionally challenging games?
https://store.steampowered.com/curator/41773079-EmpathyGames/list/91358/

There are a few other lists there, but I'm really guessing here.