Hi! Could anyone help me out with my problem, I'd like to make a carbon bath, but the most nesessery thing about this project is good looks without anything accept carbon and good enough grip so that it won't end badly. If you have any suggestions leave them here please!

A lot of cases where "grip patches" are added can be done by adding very fine sand or grit to the mix to make a rougher surface in those areas.  However, on a clear resin such as this, it will compromise clarity heavily so may not be an ideal solution.
 
Alternatively, you can get stick on grip patches specifically for baths.  Some are black, some are clear "ish".  

Warren Penalver
Easy Composites / Carbon Mods - Technical Support Assistant

I would make a test with sanding the carbon, then apply resin with a roller, and then use a salt shaker to uniformly disperse salt onto the surface. Once cured the salt washes out and only leaves the craters in the  resin behind.
It's a technique used on surfboards sometimes, but never tried it myself. Might be a nightmare to clean tho.

Carbon clear yacht finishes are often done with "nonskid" particles in clear paint like Warren suggests - but it looks ugly compared to clear finish. 

Could you mold in a "nonskid" texture using an in (on!) mold clearcoat and then layup over that?  That's a common production boat thing with sticky patterns of nonskid that you cut out and fix to plugs before layup of the tooling.  Each part comes out with a perfect molded pattern.  Might be hard finding a clear that can build thickness like gelcoat.

I have done a recent non skid on a carbon gangway for a yacht.

This non skid is a polyurethane resin sprayed with a non skid particle mixed in the resin. This particle becomes mostly clear and you can still see the twill weave through the non skid. This particle is https://international-yachtpaint.com/en/au/boat-paint-products/topcoat-finishes/intergrip .

You can also hand broadcast it onto paints, mix in paints or resins. Some people broadcast onto wet paint and then spray over this too to get a softer feel.