Doesn't a VPN slow down the speed of the Internet in Taiwan?
Yes, but very little. This is because the traffic is conducted through a VPN server, which takes time. Also, additional time and power are spent on encryption. But with a good VPN and a stable Internet channel, the difference in speed will be negligible, and it can simply be neglected.
It is important to understand that the VPN services themselves do not have slow servers, otherwise the speed drop would be enormous. But you need to make sure that the server is physically close to you. Otherwise, the traffic will have to travel long distances, which slows down the connection simply due to the laws of physics.