What does “…consider this your sign…” mean?

I think it's a (very indirect) reference to the old idea of a sign from God. Like how He supposedly tells us what we need to do with little hints in our everyday lives. And then the God part faded out over the years, leaving us with signs from the universe or fate or whatever. And then people started using it a little ironically or jokingly, and now it's just one of those things people say. If you've been thinking about maybe doing something, and you coincidentally see a mention of it somewhere online, then "that's your sign" to do it. You might as well replace "sign" with "excuse", sometimes. 🤣

"This is a message [from Fate/God/Destiny] that you should purchase yourself a new stethoscope."

It's a marketing phrase. Basically a way of saying "seeing this ad is a sign that you need to buy this product." Classic consumer manipulation.