Squeal versus groan
A high-pitched squeal that rises with engine speed is usually the belt. A low groan or whine that follows the steering rather than the engine is more likely the power steering pump or low fluid. Describing which one you hear genuinely narrows the diagnosis.
Worse when cold, better when warm
That is classic belt behaviour. A glazed or perished belt slips most when cold and stiff, then grips better as it warms. It usually means the belt is due rather than the tensioner having failed outright.
Clicking rather than squealing
A rhythmic click that speeds up with the car and only appears on tight turns is usually a CV joint on a front-wheel-drive car — a different repair entirely, and one that gets worse steadily.