I'm not aware of any "official" guidelines, but here's a list of methods I'd use to create a seamless experience:
1. Have a base design system that can be used across most screens & devices (E.g. Material Design)
The goal here is to have our customers recognize and remember common UI components and interactions across devices. Those components should scale based on the arc minute for the device. Be familiar with how to calculate size based on arc minutes and device distance.
2. Minimize custom controls within that design system for specific screens & devices, but use when appropriate (E.g. off screen slide out menu's for mobile or utilizing the back button on Android vs slide right on iOS)
The goal here is not to limit ourselves to the lowest common denominator UI components. We should be empowered to leverage each platform as necessary to delight our customers but not limit some because of the existence of others. (E.g. slide out menu's on desktop don't make sense if you have the screen real estate)
3. Consistent resource accessibility across platforms
The goal here is to not make a customer feel like moving from one platform to another ever prevents them from accessing their data. Let them decide which tool is appropriate for the job, but don't remove the assets from the job. E.g. If the customer has access to some data on the desktop, they should be able to see the same data on Mobile. It may need to be displayed differently, but it should never not be accessible. Let me decide that working with a spreadsheet on my mobile phone is frustrating and I can move to the desktop when I have time, but don't stop me from looking up data I need.
4. Match feature locations across screens & devices where appropriate
The goal is to leverage spacial awareness on one device across others. (E.g. If the menu system on mobile slides out from the left, it should be left aligned when visible on desktop. Items should be in the same order and if different, should at least start with the same first few words or the same icon.)
5. Optimize delivery of content based on device activity
If you have video content, deliver it with a black background on a TV but you might not be able to make the same assumption for delivering the same content on a Desktop so including a white background with the comments alongside the video might be more appropriate. This would be because typing comments is going to be less likely on a TV, but more so on a Desktop.
I'm sure I'm missing a lot here, but this should be a good start?