I do not have TLJ on GoG, but Steam. I was hoping someone could help me out nonetheless. When I try to use ResidualVM to select the game folder, it says that no game file exists, even though I can launch the game no problem.

Stumbled upon the same problem with the GOG Version trying to start TLJ with the HD mod. ScummVM and ResidualVM have merged now but you need the latest daily build of ScummVM for TLJ to work.
https://www.scummvm.org/downloads/#daily

Could you please tell me what should I do with this build? Place it in some folder? The gog version does not work in my case. The RedisualVM tells me, there is no game in the folder I choose.

SCUMMVM and ResidualVM have merged. But as of this post, The Longest Journey is not supported on either programs' stable versions. You will have to download the daily builds of SCUMMVM or ResidualVM which support The Longest Journey:

https://www.residualvm.org/downloads/#daily

https://www.scummvm.org/downloads/#daily

Follow the directions here:

https://github.com/residualvm/residualvm/blob/master/README.md#5-running-the-longest-journey

Enjoy!