There seem to be a few different matters for consideration.
Conflict of interest
Items 1 and 4 relate to your design and checking your design has been implemented by the construction contractor. I do not see a conflict in interest with respect to that matter. I am also assuming you do not have a financial interest in the project or own shares in the construction company (either of those could create a perception of a conflict of interest).
No matter who you are contracted by you have to operate ethically. In this case, taking reasonable steps to safeguard health and safety, report adverse consequences, and inform others of the consequences of not following advice. This is what would typically be a part of construction monitoring. I do not see any ethical issue with that.
Contractually engineers would not be doing any work without someone paying for it. Is working for a construction contractor in the role of construction monitoring any different from working for the building owner performing the same role? There may be a difference in the construction contractor wanting to comply in a way this satisfies the building consent but may not have the same long term interests as the building owner. Where those differences occur it would be best to communicate to the building owner prior to starting the contract so that they are fully aware of that being the case. Outside of that communication it appears to be more of a question of loyalty than a conflict of interest. From my perspective obeying the building act and operating ethically is more important.
That sounds a little like a power balance issue. I always listen, be fair and helpful to construction companies. However conflict can be unavoidable if someone insists on performing poorly, especially when you have given them one or more opportunities to do the right thing. At that point it’s more about how you handle an adverse situation.