What’s the brand and model of the dumb TV?
Not all televisions will turn on just because power is restored, and when you splice a relay into the power cord you’re essentially just cutting the power and then restoring it.
You can test this by unplugging the TV cord while the TV is on, and then plugging it back in. If the TV comes back on, then you can use a smart plug or a smart relay. But if the TV stays off, you can’t. Different models work differently in this regard, which is why the model number matters.
There’s also a separate issue, which is that some TVs may be damaged by repeatedly cutting the power and restoring it. You don’t hear of this happening as much with TVs as you do with smart bulbs or motorized devices, so again the TV model matters.
Also know that the reason why some people may be splicing this into the power cord rather than smartening the outlet is that that Sonoff model can only handle up to 10 amp, which is not to code for a regular residential outlet, which are supposed to be able to handle up to 15. Splicing it into the TV cord removes that issue since the outlet can still handle 15A.
If it was me, though, I would go a different direction, and get an IR blaster that works with the TV, like the Switchbot mini hub. That way you don’t have to do any wiring, you don’t void the TV warranty, you don’t have any potential fire safety issues, and installation is easy.
That said, the IR blaster method will not keep things in sync if the TV is turned on a different way so it might not work for your use case.