RGB is additive
Screens emit light: red, green and blue add together, and all three at full intensity make white. sRGB is the standard web colour space and what every browser assumes unless told otherwise.
CMYK is subtractive
Ink absorbs light. Cyan, magenta, yellow and black subtract from white paper, and all four together make a muddy near-black — which is why printing uses a separate black plate.
The gamut problem
CMYK cannot reproduce the bright saturated blues, greens and oranges that a screen can. Converting RGB to CMYK necessarily dulls those colours, and no setting avoids it — it is a physical limit of ink.
Which formats carry CMYK
TIFF, PSD, EPS and PDF do. JPG technically can. PNG, GIF, AVIF and WebP do not — WebP is sRGB, 8-bit, full stop.
What this means practically
WebP is a web format and should never enter a print pipeline. If work is print-bound, keep a TIFF or PDF master in CMYK with the right ICC profile and generate WebP only for the web preview.