Okok. Just for me to understand, why is the display showing correct colors in premiere? And knowing professional HDR color grading monitors are VERY expensive, is there any monitor under 1000$ i can use to start? Thanks a lot!
Your display is not showing "correct" colors. It is simply showing the color values as is within the capabilities of your display. The unaltered HDR data looks very flat similar to a log profile from a camera. You probably took that image as is and made adjustments based on that. When it would display as it should be on an HDR monitor, it would look very colorful already. This is partially why after export it looks super saturated and bright because the video player will do a basic conversion from that HDR video back to SDR for your display.
Hope that makes sense.
The hard reality is that HDR is quite a technical topic for beginners. You need to know quite a few things to really understand what you're doing. Buying a good reference HDR monitor is out of the question for hobbyists but a display that can produce quite a good result is actually the XDR displays from the MacBook Pros which you just may have already without considering that. But even then, you still need to consider for who you are creating content. If you will watch it back on your HDR OLED TV for example then that's very nice of course. But general content creation is for the majority still SDR because typically more than 90% of users will watch it back on an SDR display.