The "Clock" app that comes standard with the iPhone has a stopwatch function. It's easy to use, just start the clock app, open the "Stopwatch" tab at the bottom of the screen, and tap the start button. If you tap the lap button during measurement, you can record the elapsed time (lap time), which is functionally comparable to a real stopwatch.
The stopwatch will continue to run unless the user stops it, or shuts down the clock app or the system itself. It will continue to operate even if it is automatically locked, so if your goal is to measure the time, just unlock it.
If you really want to keep displaying the screen being measured, open the screen in the order of "Settings" → "Screen display and brightness" → "Auto lock" and select "None". This will keep the stopwatch visible until you close the screen or switch to another app.
If you just want to avoid automatic locking, keep looking at your iPhone screen. IPhones with X or later that support Face ID have a function to sense the user's line of sight (gaze) with a built-in sensor, and if you look at the screen even for a moment, the countdown to automatic lock will return to zero. In other words, if the automatic lock setting is 1 minute, you can avoid the automatic lock by just glancing at the iPhone once every 1 minute, and if it is 3 minutes, once every 3 minutes.
By the way, the iOS development framework has a function to prevent sleep / auto-lock, and apps that use that function can continue to display the screen no matter how many minutes the auto-lock is set. Apps that are inconvenient to be locked automatically, such as cooking recipes, take advantage of that feature, but Apple seems to have decided that it's not necessary for the clock app / stopwatch.
