Shooting a milky way timelapse on my Canon EOS 200D Mark II

You can use a remote to take the pictures. They are sometimes called cable releases or intervalometers. They allow you to adjust settings to take a series of as many images as you want. The only restriction is the size of your SD card.

There are plenty of cheap (~20$/€) ones. If you cannot find one made specifically for your camera, check that the connector is the same.

The interval-timer on Canon bodies that have the built-in feature work a bit different than an external interval timer.

External Interval Timer

An external timer can either use one of the camera's fixed shutter speeds... or can use bulb mode. In bulb mode, the timer is effectively "holding the shutter button" and releasing it to end the exposure. This means you can set the bulb duration on an external timer.

For this reason, the "interval" that you define on an external timer is the amount of time to wait after the END of one exposure until the START of the next exposure.

E.g. if you want 10 frames, 15 seconds per frame (but using Bulb mode) and a 5 second interval, the timer will take a new exposure every 20 seconds ... where each exposure had a 15 second duration.

Built-in Interval Timer

When using the built-in interval timer (on models equipped with one) the camera menu doesn't ask for shutter exposure duration. This is because it uses whatever duration is configured via the camera's normal exposure controls (be in manual or an automatic mode). But the key here is that it cannot use Bulb mode.

In this mode, the camera simply presses the shutter button at periodic intervals ... with the interval timer not actually knowing how long the exposure will take.

This means that if you know you plan to take 15 second exposures ... but want a 5 second delay between frames, you would have to add those values together 15+5=20 and then program in a 20 second interval.

In other words, the "interval" is the amount of time from the START of one exposure until the START of the next exposure.

This also means that if your "interval" is shorter than your exposure duration, the timer will not work as expected.

Other Options

As previously pointed out, you can get an external shutter release with a timer (some external releases do not have timers). There are several generic external timers but they are sometimes camera-model specific to make sure they have the correct interface cable that works with your camera model (others have the ability to swap the interface cable and can be used across many different cameras).

You can also control the camera via computer. Canon's own EOS Utility has the ability to function as an interval timer. There are numerous 3rd apps that provide similar functionality.

Summary

You might not require any external timer or computer to capture your shots ... if you were setting the "interval" duration to a value shorter than your shutter exposure duration then the timer would not have worked. If this was the case, just increase the interval duration to make sure it is longer than the exposure duration by a few seconds.