Shovel Knight is an excellent game, especially for fans of early 90s games. It's sort of like a combination of Mario 3 (overworld map and platforming), Zelda 2 (medieval setting), and early Mega Man (beating bosses for powerups). The level design is great, the graphics and music call to mind the best of the 8 bit era--honestly I could go on, but Shovel Knight sounds like a perfect choice for someone like you. Highest recommendation.
Outside of that, Stardew Valley is like a more expansive Harvest Moon but still has SNES-style graphics.
As for side-scrolling games, I've heard Hollow Knight is a great Metroidvania-type game.
Cave Story is another Metroidvania with more of a sci-fi, run-and-gun angle to it with more great pixel art and chiptune music.
Undertale is a very critically acclaimed 2D RPG with SNES era graphics. The battles are turn-based and integrate elements from shoot-em up games (you dodge enemy attacks like you would in a bullet hell game.) The gameplay is good, but the music and especially the story are really what set this one apart tbh. Highly recommended--for fans of Earthbound especially.
Super Meat Boy is a platformer that calls to mind the Nintendo-hard games of yore, although you have much greater freedom of movement than games like the early Castlevanias, and its also much more forgiving when you die (you respawn in seconds).
If you're a real masochist, or if you were a master of old NES platformers, I Wanna be the Guy is a ridiculously difficult game which takes the idea of Nintendo hard to the next level. You have 1 HP and everything is trying to kill you (to the point of comedy). Only play this one if you're really looking for pain.
Hotline Miami is a bloody, comical top-down shooter with an 80's vibe and an unusual story focused on conspiracy and misleading the player.
Cuphead is a run-and-gun game like Gunstar Heroes on the Genesis. The game is quite difficult and has a beautiful art style that makes it look like you're in a 1930's cartoon.
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Diagnoses: AS, Depression, General & Social Anxiety
I guess I just wasn't made for these times.
- Brian Wilson
Δυνατὰ δὲ οἱ προύχοντες πράσσουσι καὶ οἱ ἀσθενεῖς ξυγχωροῦσιν.
Those with power do what their power permits, and the weak can only acquiesce.
- Thucydides