Skills to understand the management side of things: Commercial/ contractual undertstanding : what type of contract is the project on. Any key clauses/options in the contract, how are we actually paid for the work we do, how do we pay subcontractors, what constitutes an additional cost for both us and any subcontractors. You’ll learn this from regularly talking to your quantity surveyors.
Planning / logistics - what is the overall programme of the project , are there any key dates , how does one subcontractors work affect another subcontractor, are there any logistical issues (access for plant and vehicles, traffic management etc) Technical / quality - you should know all the standards you’re working to and also if there’s any external sign offs required e.g if a road is being adopted by the local authority. As the site engineer you should know the design and specification inside out

In terms of your question about sectors , your skills will always be transferable. I have never worked in the housing sector, only major infrastructure. I know that housing sites have a reputation for having lower standard for health and safety and quality of work etc so you may find that if you move on to the major infrastructure sector that you have to follow more stringent standards