I managed to create my own plugin (with some or rather a lot help of chatGTP) that can do this for my sites now. When workin on this there was a bit of a struggle to get the 'active' state of a tab correctly. Joomla seems to remember the tab state on an individual item. But it default to the first Joomla tab. Moving tabs in front of the default first tab still has the default Joomla tab active when there is no 'remembered' tab state. So moving the Custom Files Group tabs to the front, before the first default tab does not activate the first tab by default.

Moving the Custom Group Fields tabs just after the first default Joomla tab does work now for me. So I happy with thsa for now.

But still, maybe an option Joomla to do this would be nice / better. The plugin I created uses javascript to swap around tabs. It works but it's not the best solution.

i did this myself with a simple layout override the other day. This blog post explains how https://www.dr-menzel-it.de/blog/override-challenge-beitrag-einreichen-im-frontend

That looks like a lot less work then creating a plugin ;-) I will give it a try.
But still, it would be a nice feature to have natively in Joomla I think.

@brianteeman I looked at the blogpost and I think that is more related to changing the total layout of the edit page (article or user). That would indeed mayb keep the backend more 'sleek' by combining all fields in one tab and / or only showing 'essential' fields. But my issue is just with the position of the tabs that are created by the custom fields.

Every custom field GROUP we create get's it's own tab in an article (or user) edit view. I just want to place those directly after the first 'default' joomla tab (For articles: 'Content'). And not somewhere more to the right.

I don't see a way to just do this with a template override. It looks like the Custom Field Group Tabs are generated with this code in the edit.php:

<?php echo LayoutHelper::render('joomla.edit.params', $this); ?>

When I put this before the first tabset in the edit.php the do show up as the first tabs. So that would work if I wanted them there. But I don't think I can put the after the first tab... So like this 'Content' - Custom Fields Tabs - all other tabs.

I also think creating overrides for all sites and adapting them to each sites needs will work for me because that would also involve more maintenance and possible issues. So maybe my plugin is more useful for me right now.

Again, it would be nice to be able to just have a setting / option somewhere to tell Joomla where to put the Custom Fields Group Tabs.

I looked at:
layouts\joomla\edit\params.php

But it's a bit much for my current skillset at this point....

I did also notice the 'Schema' tab is also generated by this layout helper. Not sure why those are combined in this layout file, but I don't understand enough about the setup to have a real opinion about is.

I don't know if this file also can have an override but I am also not sure I want to do that...

So for now I just will use my plugin solution and maybe a more skilled developer might be able to do something with this feature request. Or maybe this is not very important at all to anyone but me ;-)