What are you replying to? Your mileage may vary, but I often send youtube links for samples of past work that are relevant to what the client is looking for. A lot of my clients also send me their websites for reference. I don’t see anything immediately wrong with what the OP posted. Sometimes it’s necessary to get that information to see if we are a good fit for the project. In the design field it’s nearly mandatory if you are doing serious work.
Fiverr doesn’t have a good way to show video or web design work, for example. The portfolio feature allows videos, but the max upload size is ridiculously small - unusable. For websites, it’s just impossible - an image doesn’t show you how animations work, navigation, etc. There’s no other way than sending direct work links.
It’s forbidden to share any personal or contact information. There are no rules forbidding what the OP said.