What I can use to waterproof a sink cutout
Danish oil, tung oil, linseed oil will work if you apply multiple coats and re-apply on a regular basis. There are also special formulations with additives (waxes) that increase water and chemical resistance (but are usually less impact resistant).

Varnish will work as well, is more prone to mechanical damage, but does not have to be re-applied unless damaged or worn down.

Spar varnish (or outdoor varnish) is usually more resistant to UV and water, but will also usually emit more harmful fumes.

Solvent-based varnishes will in general be more durable and easier to apply than water-based varnishes. Water-based varnishes are generally healthier (less emissions and toxic fumes).

Most danish oils are food safe and will increase the hardness of the surface (offer better impact protection).