Why can't my laptop find my Wi-Fi?

I recently got a new wireless router with a new contract. It's a Fritz! Box 1&1 Homeserver + with matching 1&1 contract. Neither my cell phones nor the television nor the Amazon Fire tv stick had any problems connecting to it. My MSI GL72 6QD built in 2018 just can't find it. However, he has no problems with other networks. It works when I use an ethernet cable. My sister broke that, and that doesn't make sense with WLAN either.

Wi-Fi is not approved - this is usually the case with new devices

Download the https://de.msi.com/Laptop/support/GL72-6QD from the manufacturer's website and reinstall it. Furthermore, you should then shut down the laptop completely and also disconnect the router from the power supply for about a minute.

After restarting the router, it can take several minutes before the connection to the Internet can be re-established, so be patient!

But I don't have the problem with any other new device. I just dug out my old iPhone 5 and connected it without any problems.

But how should I do it best without an internet connection?

This can also be done via a friend's network or a cell phone, for example.

That sounds like the simple explanation that you have no reception at the location and with the antenna alignment (which is logically not identical to your FireStick).

If your sister should have done something (you don't tell us what that should be) you should have it repaired.

Basically, almost 100% of WLAN problems can be traced back to the fact that the user is not familiar with the physics of the spark (although they want to operate a radio) or that the device is physically defective.

What broke is the Ethernet cable that you attach to the router and to the laptop or other device to have a direct connection. You don't need the cable for a Wi-Fi connection, but only for the Ethernet with a third device.
And I've already tried to sit down with the laptop right next to the router, which doesn't work either. In the meantime I have borrowed a repeater, which I have connected to the WLAN and my laptop can establish a connection to the repeater mentioned. But he still doesn't want to do that directly to the WLAN.

What broke is the Ethernet cable that you attach to the router and to the laptop or other device to have a direct connection.

Good. That didn't come out exactly what your sister broke.
This information is completely irrelevant - especially since such a cable can be replaced with a few euro.

But he still doesn't want to do that directly to the WLAN.

Then read my answer again carefully.
I have explained the usual causes in this case.

Not at all.
You wrote that your laptop works in other WLAN networks.
Therefore it can't logically be a driver problem.

It has often happened in the past that certain adapter chips could not work with one another. Therefore you should always keep the drivers up to date; it makes sense to install a different driver.

It is indeed worth a try - but if the adapters are incompatible on the hardware level… Well, at least I keep the probability that it will help at almost zero.
But as I said, updating drivers is always worth a try.