Or, if you wanna sound intellectual: „Das tangiert mich peripher.“

No, HDR can’t make your monitor brighter than it is. But it can take full advantage of the brightness and contrast of modern displays in a way SDR cannot. In almost every case HDR looks better than SDR but brighter and/or more contrasty displays take the most advantage.

In a more technical sense, SDR content is mastered with a peak brightness of 100 nits in mind. HDR is mastered for a peak brightness of 1000 nits, sometimes 2000 nits and the resulting improved contrast.

If you don’t watch movies in HDR on a modern TV, you’re not taking full advantage of its capabilities.

That’s incorrect. While it can be assumed that HDR content supports at least 10bit colour, it is not necessary for monitor or content. The main difference is contrast and brightness. SDR is mastered for a brightness of 100 nits and a fairly low contrast. HDR is mastered for brighnesses of usually 1000 or even 2000 nits since modern displays are brighter and capable of higher contrast and thus can produce a more lifelike picture through the additional information within HDR.

Of course you need a sufficiently bright and/or contrasty monitor for it to make a difference. An OLED screen or displays with a lot of dimming zones would produce the best results there. But even a 350nit cheap TV can look a bit better in HDR.