Religion tends to provide a framework for the teaching and consideration of morality.

I would argue that it is being human that provides a framework for the teaching <!and learning--> of what we call morality. We are hardwired to assess the society and family we find ourselves in for friends and foes, opportunities and dangers. There is no known society in existence today that does not have a set of moral teachings attached to various creation myths, etc. that loosely cohere into a worldview that supports the social structure.

It also suggests that you are being constantly watched over and your actions assessed.

Again, being human is the precondition, not being religious. We have competing brain modules/processes where there are assessments being made about all types of things in our world. Most of this happens outside of our consciousness but some of the bits that float into the consciousness have been "judged" or watched over by the "superconsciousness" modules of our own brains and we can sense this.
There is also the theory of 'tricking ourselves' into being sincere as a way to convince others that we are not a cheater and are serious about something we are doing.
I can also imagine how the assignment of agency to inanimate objects in the environment, a process of pattern seeking (making?) would reenforce the feeling of being watched over.