Yes it is the same, HLG does not seems to be different before and after the encoding.
What is very strange is that even when I'm using the Premiere encoder to output in HDR PQ the colors are pretty the same...
I need to test all the encoded files on screens supporting HLG and PQ to see if there is any difference.
The problem is, Premiere is reading your HLG file as SDR. That's okay if you turn around and export as HLG, but the native export will be HLG displayed as SDR, encoded in an HDR container. Just like you could encode any SDR video in HDR mode through premiere's HEVC codec if you want.
HLG is designed in a way that if you read it as SDR, it still looks fairly good, but the colors being the same is an oddity. If the source has BT2020 colors, then Premiere would likely decode that into rec709 color space, meaning you'd need to perform a conversion using the colorspace filter to fix this (input rec709, output bt2020), and then select bt2020 and HLG options in x265 for correct output. Or skip the colorspace filter and use HLG paired with rec709 colorspace and primaries, although that's not recommended.
However, if Premiere is just ignoring the color space, then you may be seeing the native rec2020 color space, which SHOULD look slightly weird in the preview monitor. Like slightly desaturated, maybe a little yellow tinted. If that's the case then you would be free to encode to x265 with HLG and bt2020 options without using the colorspace filter.
Do you have a sample source file I could test? I could maybe give you some advice on how to encode it properly.