Two main exceptions:
1 - if you are letting the property to someone else, e.g a lodger or have paying guests staying with you then this is typically excluded.
2 - if you have had previous theft claims, live in a high crime area, or you have a particularly high risk (e.g lots of valuables), the Insurer will add an endorsement that you need a minimum standard of locks and have them engaged when the property is unoccupied.
Outside of those, if you accidentally leave a door unlocked, your claim will likely be paid. The situation obviously may be different in other countries. I worked for a property insurer and saw hundreds of these claims (entry via an unlocked entry point) paid during my time there - I also saw many declined because of the above.
I suspect that over time the number of policies in the 'budget' category will continue to increase as price continues to trump everything else for most people]
edit: it is the same for the other lines I mentioned as well -e.g a cyber policy I saw recently has no conditions relating to use of MFA. It will have been factored in when writing the risk (they will have said they use it) and if it turned out it was a lie then there would be an issue with cover but if it was just a case of an admin forgetting to include an OU in the MFA group policy the claim would almost certainly be covered. Policies aimed at the SME space are much more likely to have specific conditions though.
How is this supposed to be assessed? You can demonstrate that a door was locked, if some kind of obvious measure was taken to circumvent it (destroying the lock, destroying the door, destroying the window...), but you can't demonstrate that it was unlocked. Burglars aren't limited to destroying things to bypass locks. One obvious approach is to pick them.
All that said, I can't recall many instances where the theft wasn't either breaking and entering, or entry through an open access point. As easy as lock picking might be, it's not a common burglary technique.
Is that commercial or residential?
I've never seen a residential insurance that requires an alarm system, let alone a monitored system. Though many carriers will offer a discount for having this.
Where is here? I'm not aware of that being common anyplace in the US. I'm guessing you're in some country where crime is significantly higher than in the US.
I’m pretty sure this will be the same for the other insurance you mentioned but for property insurance if you left your front door open you will have a hard time getting the insurance to actually pay out your claim. At least here they require a burglar alarm and they require it to be armed when nobody is on site or they will absolutely decline the claim.
Insurance insures against risk, but there’s a threshold to that and if you prove to be above it they will decline your claim or void your insurance in totality.