Is there a glove which is slip-resistant, cut-resistant and resistant to hot grease? Hoping there is a product in the industry.
Like any kitchen tool, a protective glove is only as good as the skills of the person using it. I know chefs who swear by cut-resistant gloves and others who do not allow them in their kitchens, feeling that they encourage sloppy habits. Personally, I like having them for repetitive tasks that are particularly hazard-prone like shucking oysters, grating with a box grater, or slicing on a mandoline. The risk of being overly reliant on cut-resistant gloves, of course, is that it can build false confidence in cooks that can be as dangerous as the exposed skin.
Most food-safe cut-resistant gloves are made with a strong mesh of material such as polyethylene, Kevlar, or even steel. While they provide some protection against heat, as most fabrics would, they will not protect against high temperatures, steam or hot liquids.
There are heat-resistant gloves that are designed to be both heat- and steam-resistant (though not waterproof) and can also protect against cuts. It is probably the closest thing to what you have in mind. However, the tradeoff for finding a glove that can meet all your safety needs may be sacrifices in lightness and dexterity.
Most of these gloves are relatively affordable, so my advice is to try them. Be sure to add them to a foundation of good skills so that your culinary skills protect you from cuts and heat and your gloves are insurance, rather than relying on them to regularly get between you and knives and flame.
More on what to look for in cut-resistant gloves here.