Can you please upload the minimal project here, so we can confirm and identify the issue. Also, based on your writing I assume you used the cable export of QFieldSync, not QFieldCloud. If my assumption is correct, can you please confirm that opening the packaged version appear incorrect also in QGIS, or it is only a QField issue?

you're right for both things: I used the cable export and opening the zipped project in QGIS appears incorrect (i.e. with an empty group named "RASTER BASE").

BTW, trying to pack up a minimal project with the same settings and -partly- data, now I get an error saying "No basemap layer selected. Check configuration"...even though basemap is set to use a style merging the two layers within the RASTER BASE group.

At this point, the idea is to do a total reinstall of QGIS but, before doing it, I ask you: shall I or you prefer to keep the system like this to find the bug?

Please provide us a sample project, so we can confirm your issue.

Two things you can check before reinstalling:

1. create a new QGIS profile (don't delete the old "broken" one) and see if you experience the same.
2. if you are a Windows user, you can install multiple QGIS versions in parallel and see if you experience the same.

OK, I'll do in the next days. In the meantime I attach here the minimal project for the second issue (no basemap)

Uploading minimal_project_NoBasemap_Selected.zip…

The QFieldSync project highly values your report and would love to see it addressed. However, this issue has been left in feedback mode for the last 14 days and is being automatically marked as "stale". If you would like to continue with this issue, please provide any missing information or answer any open questions. If you could resolve the issue yourself meanwhile, please leave a note for future readers with the same problem and close the issue.
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If there is no further activity on this issue, it will be closed in a week.

Please provide us a sample project, so we can confirm your issue.

Two things you can check before reinstalling:

1. create a new QGIS profile (don't delete the old "broken" one) and see if you experience the same.

2. if you are a Windows user, you can install multiple QGIS versions in parallel and see if you experience the same.

my experience remained the same and I'm not able to create a smaller project for testing this issue...I guess it's related to the project itself.
In the meantime I opened a new issue for the other problem.

The QFieldSync project highly values your report and would love to see it addressed. However, this issue has been left in feedback mode for the last 14 days and is being automatically marked as "stale". If you would like to continue with this issue, please provide any missing information or answer any open questions. If you could resolve the issue yourself meanwhile, please leave a note for future readers with the same problem and close the issue.
In case you should have any uncertainty, please leave a comment and we will be happy to help you proceed with this issue.
If there is no further activity on this issue, it will be closed in a week.