As far as "code" is concerned, AFAIK, a water heater has never been classified as a boiler, at least as far as the residential style domestic water heater is concerned.
Additionally, people do not change the water heater T&P valve to one that is rated properly for boiler use, which is a bigger problem, IMHO.
If your boiler has a standing pilot, leaving it on can keep the spiders away.
Some circulator (pump) controllers have an exercise function, which will help keep the circulator from seizing due to a lack of use. Depending upon the size of it, it may not be too expensive to simply leave it on... or make up a timer control. Leaving the pump on can prevent pipe freezing if there's a cold snap after the system has been turned off and it is forgotten to turn it on for that day.
Otherwise, if there isn't a call for heat, it shouldn't operate, which means it is off. Killing the main power will just kill standby power usage by the board or 24v transformer.
Both my buddies son and my boiler systems are in a detached garage not our homes.
My system has been turned off about this time of year and turned back up in the fall. So not likely to have a freeze up situation as there is glycol in the tubing. So only used for heat and not required for heating water. I’d be more afraid of items in garage freezing and that would take some time.
When I turn it down both the 120 and 240 volt breakers are turned off.
I run my IBC boilers in the fall for a week and shut them off and heat things with my outdoor wood stove until spring when it gets too warm for the wood stove to run without turning into a creosote factory. At that point if I feel (let’s be honest here, if SWMBO feels) like we still need the heat on I’ll turn the boilers back on and let them provide heat. I will always run them at least a few days in the spring to make sure they’re still operational as they’re my backup heat source if the stove goes down for some reason. I’ve never had an issue with the boilers turning back on either spring or fall.
Zero reason to leave them powered up in my opinion. I flip breakers and walk away until fall.
An easy solution wood be to run the boilers weeks before you “need” them and you should have time to get someone out to service them if needed.
My boiler is also an IBC, my back up are the days when it the days hit a nice light jacket day outdoors and the door can be left open. Haven’t turned it down yet, but the days are getting warmer. My garage is R24 in the walls and 8” Styro on the roof. I did the insulating my self and carefully installed and sealed. Garage doors are R18 and fit snuggly.
I’ve seen a couple of examples of your heating system and if I was on the farm that would be my go to.

Good job. I never really thought of a low smouldering fire causing creosote, interesting point.
I’m in your camp as to turning the system down when not required.
Funny story, but not really. I’m in the garage and it felt cool never gave it any mind and didn’t check it out. Got busy and forgot all about it. The next day it still felt cool. Found my thermostat batteries had given out. It was probably 25-30C outside, needless to say it took awhile to build up the heat sync in the slab. I keep it around 60F and depending on what I’m doing it can a bit much. But great for having a buddy over and enjoying a beer.
Regarding the buddies son, his water heater may be indirect fired, meaning there is a heat exchanger in the water heater pulling heat from his hydronic boiler. If this is the case, his boiler needs to be on all the time.
That might be the reason. My buddy is a boiler maker and is out of town on jobs so I’ll have to quiz him next time he is home. His son bought the place with a detached garage and water heater setup. Water heaters may have been allowed in detached garages at one time but no longer. Maybe he is not using glycol and doesn’t want to take the chance. My contractor said he could setup my lake garage with a water heater setup, I’ll think I’ll pass. The gas inspector said I could use an on demand setup if I had a use for hot water by having a bathroom installed. So that won’t be happening at the lake but I had lines run in case I do a boiler setup which I’m thinking about but will have a NG blower at the minimum.
That is how it was plumbed in my last house. Boiler was required to be operational year around, if you wanted hot water for showers, etc.
In a house I totally agree. My application is a detached garage. My one neighbour or maybe it was his wife had a total reno of their house. They even did a portion of their driveway and piped that needed to be replaced. She thought she could free up some space until she found out that the ac needed to be dealt with.

They also have a detached garage with a NG blower. Knowing her I thought they would tear up their garage floor and place tubing. They did do a chunk of driveway so why stop there.
