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This.
We have a wood drainer area, but it has a £50 draining rack on it. 5 or 6 years down the line and zero stains (does get looked after though). Check about 100 pages ago, went into detail along with a few other folk on how to get wood tops from new to epic, and rescue them from that kind of a state. IMO (but maybe not correct!) wood 'finish' is very important, just sanding to 240 grit is nowhere near enough, you need to keep going, 600-800-1000/1200 sort of grade, fine wire wool it, dedust it etc. Then work up through the oils. Months from now when its all proper soaked through and hardened, go at it again at the high end 1000+ and some fine wire wool, clean with meths then osmo seal it with whichever variety you like.
Mines seen lots of use for sure, gets cooked on every day for up to 4 people, 4 bike people too so thats a lot of food, only thing that ever stained it was some kind of super alkaline cleaner for the oven, but sanded it out.
Wouldn't bother with varnish, as soon as you get a cut into it, surface blows.
We use 'tongue' oil, or at least one brands version of it, great colour on unstained oak, however its borderline useless as a sealant, without the osmo it would look rank or stain within 3-6 months.
If you have the space I'd recommend a single bowl sink with integrated drain boards on either side. I'm biased because we inherited something like that in the form of porcelain over steel, but I've never seen anything that appeals more for functionality and long term durability - ours is from the 30s and aside from a couple of chips it's in great shape.