can you tell me how to do it then? do i use ethernet cable? or does it have to be the laggy wifi method mentioned in post 2?
Apps or services that allow it to function as a secondary display over WiFi is the only cheap and easy solution - and lag is unavoidable, as the video signal not only has to pass through at least one, possibly two wireless signals (source -> router -> SP3), but also has to be compressed at the source and decompressed on the SP3. Every additional step introduces more lag, and WiFi is notoriously unstable and sensitive to interference.
Something that
might allow you to do this with less lag and compression is to use a USB capture device. I just tested my Elgato HD60s, and when connected to my desktop I can extend its desktop to my laptop's display by using Elgato's capture utilities (without actually recording anything). Lag was perfectly acceptable, couldn't see any perceptible lag when typing on the secondary display - but then the HD60s is advertised as giving "instant capture previews", so that's part of what it's made for. Of course, this is a costly solution - the HD60s is $180 on Newegg, and the cheapest thing I can imagine working with the full resolution of the SP3, the Cam Link 4K, is $130.
It's also worth noting that just displaying a static, empty desktop at 1080p60 on my laptop from the HD60s represents a ~20% CPU load and a ~20% GPU load on my laptop's i7-8650U in the standard capture utility that AFAIK only supports up to 1080p60. In the 4k capture utility, GPU load for the same stream hit 70% for some reason. A Surface Pro 3 might struggle with resolutions matching its native resolution, in other words.