Thank you for your feedback, I have discussed the situation with other engineers.
I understand the inconvenience this issue has caused you.Based on your description, this issue may indeed be a short time problem, but the community support forum has no way to contact Sway's team to confirm the situation, so perhaps the issue will be resolved soon.
Please try switching networks, such as connecting to a cell phone hotspot, and then try again to see if you can embed the video;
In the meantime, I suggest you post this in the Sway section of the Feedback Center and send me a link to your feedback, and I'll call on people around you to vote for your feedback, which will raise the priority of this feedback and bring it to the attention of the Sway team sooner rather than later.
Here is the link to the Sway feedback:sway Embed video code · Community (microsoft.com)
Thank you for your patience and time on this.
Arthur - MSFT | Microsoft Community Support Specialist