Schlage Encode Plus deadbolt works well. Many locks have an auto lock timeout. Some have homekit or google assistant integration so that you can create some automation that locks the door when you leave. You can also get notifications from the lock.
Home Automation
Home automation is the residential extension of building automation.
It is automation of the home, housework or household activity.
Home automation may include centralized control of lighting, HVAC (heating, ventilation and air conditioning), appliances, security locks of gates and doors and other systems, to provide improved convenience, comfort, energy efficiency and security.
Warning: Working with electricity can result in injury, property damage, or even death if it is not done properly. Please keep this in mind while assisting others. If you are not sure about what you are doing, hire a licensed professional.
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Any smart lock will have the ability to be opened remotely. That is the smart part. But some will be only via their cloud app. Ideally you probably want a local solution. If so, avoid any WiFi options.
There are plenty of non-smart electronic locks that allow you to have a wired remote release.
I've had a Trilogy T3 in my house for 2 decades. It is a keypad lock, not smart. But it has a remote release wire that I connected to a smart relay. This allows me to open my door remotely without having to trust that some lock company got their digital security right when eve big tech companies fail.