It'd be extremely difficult to make a crossing of the bering strait work practically.

It's not just the technical challenges of building a bridge or a tunnel in pretty harsh conditions. It's also that on the russian side there is a huge area that has almost no human settlements and no infrastructure. You'd have to build a train line through an area of nothing. That also means it's difficult to imagine intermediate steps (e.g. first building half the rail line to even get there).

The North American side isn't much better. There's ~1000km from the Bering Strait to Fairbanks, which is the nearest road/rail connection in Alaska. But the Alaska Railroad isn't connected to the rest of North America--you need another ~1500km to connect to the railheads in Canada that would let you travel to any major city in North America. (By comparison, the Russian side is ~2800km from Yakutsk to the Bering Strait).

It should be noted that just because there's no major settlements in a vast area doesn't mean there's nothing there. The Alaska/rest of North America rail connection is constantly being proposed on the basis of being able to hook up mineral extraction operations in the region, although these are marginal enough that the proposals keep falling through. Similarly, the Yakutsk-Magadan region once hosted several industrial concerns along the highway there, but the fall of the Soviet Union caused those production centers to lose viability and collapse.

The fact that Chukotka is sparsely populated wouldn't be such an obstacle in itself. It could even be advantageous = no NIMBYs preventing the construction of the railway. The intermediate steps are manageable - after all the Transsiberian Railway was built in the wilderness in the 1890s and early 1900s with much more primitive technology than is available today.

But the terrain between Yakutsk / Nizhny Bestyakh (the closest rail terminus) is pretty bad, bad enough that the construction does not make economical sense at all. The soil moves during the thaw/freeze cycle etc.

The Russians did the same when they built the BAM (Baikal-Amur Magistral).

Luckily you could transport the stuff you need by rail.

By the notion of distance from the article (great circle distance around the earth), Lisbon to New York is considerably shorter than the current record.