Maybe minutes was hyperbole, but my Sony Smart TV (to be fair, it's the circa-2015-ish one relegated to the bedroom today) is unresponsive to silly human concerns like "changing inputs" or "adjusting volume" for a good 30-40 seconds when it turns on. ("Please wait.")
To mitigate this, you can pick a certain 4-6 hours of each day (24h isn't allowed) during which it'll make sure to stay "booted" but with the panel off. Or if you don't enable this, you'll enjoy lower power consumption but have to deal with this foolishness every time you turn it on.
My smart tv is set to turn on and switch to the Apple TV when the Apple TV wakes from sleep. The tv turns on in about a second, waits for a few seconds, and then waits five seconds to switch to the Apple TV.
Same except mine goes black a few times trying to negotiate with the HDMI source. Whole process from turning on my TV to watching something on it takes 1-2 minutes.
None of them, because the Linux computer on TV boots up and goes to sleep immediately upon being plugged in, and is connected to an internal video mixer chip rather than managing the panel directly.
To mitigate this, you can pick a certain 4-6 hours of each day (24h isn't allowed) during which it'll make sure to stay "booted" but with the panel off. Or if you don't enable this, you'll enjoy lower power consumption but have to deal with this foolishness every time you turn it on.