I've used an egg in a radiator before, and glitter, and black pepper. I'm not adverse to home remedies.
But for the cost of the small box of black pepper that lasted a few days, I bought a tube of radiator sealant (Bars leak) that has lasted 25 years (I still have that old MGB, it doesn't run but the radiator is still full)
Tire sealants like Slime are a generally latex compound or equivalent with some form of media to plug larger holes. That media often consists of larger chunks of a solid rubber along with supporting fibers like cotton.
you could make your own. but getting the ratios, sizes, and material combinations right is a science, researched by an R&D lab who spend a large amount of time and money experimenting, then years of "consumer lead product testing" (letting the consumer use it, revising it as issues come up) to get it right. You would need blind luck, or a budget of millions to make something just as good.
And the cost of a bottle of Slime is about what the cost of the materials to make it your self would be, give or take a couple bucks.