It's highly unlikely to be a problem leaving the tankless water heater on, but it's a safe precaution to shut it off if you shut off the water.
The tankless needs to see flow to turn on, so it likely won't fire when your water is off. But if anything happens, someone opens a faucet or something, or air seeps in, there could be something confusing the heater and it fires up without flow. That could cause damage. While very unlikely, it can't hurt to just turn it off.
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