But wait, Xbox 360 Controllers can be detected just fine by DInput-only programs (it's a built in compatibility layer that Microsoft included in their drivers). In Dolphin your controller should've appeared as XInput/0/Gamepad but as you said it only appears as DInput/0/blablabla I guess x360c messed up everything. Also, changing from DInput to XInput in Dolphin configuration won't have effect in other softwares, only in Dolphin...
Avell A70 MOB: Core i7-11800H, GeForce RTX 3060, 32 GB DDR4-3200, Windows 11 (Insider Preview)
ASRock Z97M OC Formula: Pentium G3258, GeForce GT 440, 16 GB DDR3-1600, Windows 10 (22H2)
ASRock Z97M OC Formula: Pentium G3258, GeForce GT 440, 16 GB DDR3-1600, Windows 10 (22H2)