Looks like if we do not have enough power for a searchlight turrets upgrade,
or if some turrets are in a "distance to finding turrets to boost" radius, but are not covered with power poles - it disables that turrets ("disabled by script")

Could you just enable them in a standard mode (standard ammo & radius),
Also, some turrets can work without power at other targets in the swarm waves.
For example: the searchlight find some target far away, we have no power for near turrets, but an another wave coming right under walls and that turrets.

To be honest, I was expecting an increase in power consumption from the searchlight tower itself (or the entity under it), because when I place turrets that do not require power, I do not expect to suddenly see energy consumption on them (I did not cover them with power poles)

Originally, I intended to make turrets themselves cost power to make players have to think about their formations and plan to have some turrets explicitly not in range to be boosted.
But you make some good points.

I think I will change this, even if it takes a fair amount of time and maybe affects performance a little.
Sorry I can't give any estimate on when I'll make an update on this.

Also, I think you better review the power priority for the searchlight / turrets: I think it should be like for radars - the lowest priority.
Now it can simply stop all your factory (all assembling machines has a "no power" icon).
For me, the searchlight looks more like an optional feature, that can upgrade your turrets to fire far away. It is not a TOP feature you want have over others.

Set the power consumption priority to tertiary/secondary.
Take a look: https://wiki.factorio.com/Types/ElectricUsagePriority

Thanks, I'll consider making the energy usage priority an option.

I have released version 2.1.0 which makes turret-boosting draw power at lower priority, and no longer disables boosted turrets when out of electricity.

The new version should start to appear in the mod portal shortly.
If you don't see it in-game you can download it manually here: https://mods.factorio.com/mod/SearchlightAssault/downloads