united-states
Given a workplace IT system which is necessary to complete one's job
duties, what rights, if any, do you retain as an employee to withhold
your consent?
Essentially none, unless you personally, or your union, negotiated a contractual term for your employment that provides otherwise.
You have essentially no legal rights to privacy from your employer about what you are doing while you are on the job.
U.S. states vary considerably, in contrast, regarding how much information an employer can ask about your activities when you are not at work.
For example, employers in most states are not allowed to ask about how you voted in an election for public offices. Similarly, most Colorado employers are not allowed to discriminate against employees based upon their lawful away from work activities (like smoking).
IT monitoring is particularly common in the finance industry to discourage embezzlement and other forms of financial fraud. I have a relative who works in the back office of a bank who is required to take a complete two week vacation with no remote work every year to allow auditors to review their computer files and work in a context where the employee doesn't have any ability to interfere.
Sub-question: by extension, could an employer require an employee to
consent/agree to a physical search?
There are jobs, such as working in a mint (i.e. a manufacturing facility for coins), working in gold or diamond mines, working in factories that manufacture controlled substances, working in advanced biotech labs, working in secret national security facilities, and working in prisons and jails, where this is common. As a practical matter of employee satisfaction and finding a way to hire new employees, it isn't very common where the need to do so isn't obvious, but it isn't legally prohibited.
Other Examples
Law enforcement officers, meanwhile, are frequently required to wear body cameras on the job.
Truckers and delivery people often have GPS systems that report back to headquarters to monitor their every move and speed at all times and dash cams. Bus drivers often have this monitoring and also constant security cam and dash cam monitoring. On airplanes, the "black box" records everything done by the pilots and everything said in the cabin for a certain period of time before a crash.
The U.S. President's use of computers and communications on the phone are tightly monitored and recorded.
