Games like Invasion
Games like Invasion include LUFTRAUSERS, Vampire Survivors, Super Hexagon, The Binding of Isaac: Rebirth, and Cuphead. We matched them by the tags players give Invasion on Steam (Action, Indie, Arcade, Bullet Hell, and 2D): closest matches first, and among equally close ones the better-known games.

LUFTRAUSERS
Shared: Indie · Action · Arcade

Vampire Survivors
Shared: Bullet Hell · Indie · 2D

Super Hexagon
Shared: Indie · Arcade · Difficult

The Binding of Isaac: Rebirth
Shared: Indie · Difficult · Replay Value

Cuphead
Shared: Difficult · Indie · 2D

ZeroRanger
Shared: Indie · Action · Bullet Hell

Exit the Gungeon
Shared: Indie · Action · Arcade

Savant - Ascent
Shared: Action · Indie · Shoot 'Em Up

Hollow Knight: Silksong
Shared: Indie · Difficult · 2D

Star Saviors
Shared: Action · Indie · Bullet Hell

Hotline Miami 2: Wrong Number
Shared: Action · Indie · Difficult

A Dance of Fire and Ice
Shared: Indie · Arcade · Difficult

Hotline Miami
Shared: Action · Indie · Great Soundtrack

Planes, Bullets and Vodka
Shared: Action · Bullet Hell · Arcade

Hollow Knight
Shared: Indie · 2D · Difficult

Touhou Tenkuushou ~ Hidden Star in Four Seasons.
Shared: Bullet Hell · Indie · Shoot 'Em Up

The Binding of Isaac
Shared: Indie · Action · Difficult

Ikaruga
Shared: Arcade · Bullet Hell · Action

Geometry Dash
Shared: Difficult · 2D · Singleplayer

Jet Lancer
Shared: Action · Indie · 2D

Touhou Koumakyou: New Classic - the Embodiment of Scarlet Devil
Shared: Bullet Hell · Action · Shoot 'Em Up

Bit Blaster XL
Shared: Bullet Hell · Arcade · Shoot 'Em Up

Just Shapes & Beats
Shared: Bullet Hell · Indie · Action

Touhou Fuujinroku ~ Mountain of Faith.
Shared: Action · Indie · Bullet Hell