Defining a vanilla group in the creative_group inside of menu_category doesn't do anything while defining a custom group name will work properly. When a vanilla group is used it will default to the bottom of the category like other custom blocks.
I know this is supposed to be a supported feature because the blockbench block wizard was made in close association with mojang themselves and it also features putting vanilla groups (Doesn't work either)
Vanilla Group:
// "menu_category": { "creative_group": "itemGroup.name.planks", "category": "construction", "is_hidden_in_commands": false }Custom Group:
// "menu_category": { "creative_group": "ihg:custom_category", "category": "construction", "is_hidden_in_commands": false }Below I attached a pack showing this bug in action. One block has a custom group and another has a vanilla group defined of planks. Note: Custom groups only put all the blocks with that group beside each other, not the collapsible groups vanilla uses. Both of the custom blocks will be beside each other due to the block with the vanilla group ignoring the vanilla group and defaulting to bottom, exactly like unspecified blocks are. The pack works in both release and preview and uses 1.19.40 format version. The pack was tested with a 1.19.50 format version and received the same results.
I also included a screenshot of the blockbench entity wizard to show this is a intended feature and the two block files for easier viewing.
You called the field "creative_group" in the example files, when it should be just called "group". That's also what the Block Wizard exports.