@Milosava
"I opened the Packing Custom Tool Options and changed the mode or whatever from Unfold 3D to Recursive packing."
I am glad its working for you now, but for Max 2022 and Max 2020, changing this option to Recursive Packing did not affect Pack:Custom packing only the selected UV islands for me. Maybe this behavior has changed in Max 2023 and I don't know whether it is intentional or a bug but the docs only say that Recursive Packing "Packs the clusters efficiently, but is slower than the Linear method." Maybe someone from Autodesk can provide insight on this.