With a big antenna array for beamforming, sure, you can do that. You absolutely cannot do over the horizon radar on 10 watts with two omnidirectional antennas though.
Wait, who is doing WSPR at 10 watts? Most people are just using an unamplified IO pin off their Raspberry Pi or something; milliwatt at best.
(It makes WSPR itself all the more impressive, however!)
If you have an SSB radio that you can hook up to a PC's sound card using VOX to activate the transmitter, you can use WSJT-X or similar software to do lots of digital modes like WSPR, PSK31, FT-8 and whatever's hot these days. I think best practice for WSPR is to keep power low though, so don't go crazy :)
While there are a lot of folks using very low power on WSPR, there are also a lot on HF doing so with 100 watts, and even more in some cases.
The 'Russian woodpecker' and the US' OTH-B systems built decades ago used pulsed signals of 1 Million watts and up, with gigantic antenna arrays. [0] Comparison to WSPR is impossible (esp. given the complete lack of non hand-wavey details in the article). If the method were at all feasible, it'd very likely be commercially available).