I saw that my laptop has an HDMI connection, but I connected it to my laptop, but somehow it doesn't work, I do something wrong, I have to download something
PCs and laptops usually only have screen outputs.
So you connected the Nintendo Switch to an HDMI output.
If you want the image of the Nintendo Switch to be displayed on the laptop screen, you need an HDMI input for the laptop. You can retrofit one of these with a capture card, which then e.g. Connected to the laptop via USB.
Then you need a program that shows the signal of the capture card on the screen. Depending on the capture card, the manufacturer provides such a program.
It's a bit more complicated. Most laptops and yours only have an HDMI output. That means you can connect your laptop to a TV or monitor. However, in order to view the image signal of the switch on the laptop screen, your laptop needs an HDMI input. As long as the laptop does not have this, the switch can't be connected to it.
Just look for your question and you would have found out that an HMDI connection is a one-way street, the laptop has only one HMDI output, which can be connected to a monitor or television.
To get a picture from a console on the PC you need a TV / Capture Card
HDMI connections can also send sound in the other direction.
I checked, yes sound can be transmitted in both directions, the connection must be able to do this. A laptop can only output image and sound in one direction.