The problem with the Kuala Lumpur-Singapore high-speed rail route is how to handle immigration and customs control Malaysia and Singapore. That’s the big holdup on that high-speed rail project.
I’ve had my passport checked a few times on trains by agents who board at one station and depart at another to switch back in the other direction.
With the Eurostar, they do passport control before you board, as I understand the process. I did something similar decades ago - went through US customs in Toronto before flying to the US on a transfer there from Europe.
https://en.wikipedia.org/wiki/Kuala_Lumpur%E2%80%93Singapore_high-speed_rail