Thank you again for your help, I do appreciate your comments and suggestions.
When I initially read the post, I thought fetching was on the user as I have never seen it on the Group. Open Directory Utility, select the Directory Editor tab, and set the Viewing popup menu to Users. Find your account name, select it and look at the primaryGroupID. It should be 20 (Staff).
PrimaryGroupID: 38231146 <-- not exactly 20 indeed !!!!
Now that "fetching" disappeared, "staff" is replaced by "XXXDOMAIN" the Network Account Server of my lab.
The problem occurred when I tried to copy the whole content of an external HFS+ drive (archives from by old Macintoshes) to an external APFS drive. The copy of an old TimeMachine archive failed and then "fetching" appeared for folders in both external drives and also in the SDD of my computer. At the time of the copy, I was connected to my lab through a VPN. Disconnecting the Mac from the network did not restore a normal behaviour.
I am afraid that reinstalling macOS + TimeMachine won't cure the problem since my TimeMachine archive is probably damaged too.
In the Sharing & Permissions pane, option-click the + button. You will have access to every entity in the directory.
I tried that on /Users/myaccount. "staff" is now present but the gid is still wrong.
-------- Here more details on the present status of my account --------
Users
System
Library
Applications
myaccount
Group & permission
myaccount (Me) Read & Write
[staff] <---------- Missing!
everyone Read only
otheracoount
Shared
My current account
$id
uid=1191350732(myaccount)
gid=38231146(XXXDOMAIN\Utilisa. du domaine)
groups=38231146(XXXDOMAIN\Utilisa. du domaine)
12(everyone),
62(netaccounts),
79(_appserverusr),
80(admin),
81(_appserveradm),
98(_lpadmin),
33(_appstore),
100(_lpoperator),
204(_developer),
250(_analyticsusers),
395(com.apple.access_ftp),
398(com.apple.access_screensharing),
399(com.apple.access_ssh),
400(com.apple.access_remote_ae),
701(com.apple.sharepoint.group.1),
702(com.apple.sharepoint.group.2),
703(com.apple.sharepoint.group.3),
704(com.apple.sharepoint.group.4),
705(com.apple.sharepoint.group.5),
106005411(XXXDOMAIN\xxxxxxxxxxxxx),
then a list of XXXDOMAIN accounts
Other account
$id
uid=501(otheraccount)
gid=20(staff)
groups=20(staff),
12(everyone),
61(localaccounts),
79(_appserverusr),
80(admin),
81(_appserveradm),
98(_lpadmin),
702(com.apple.sharepoint.group.2),
705(com.apple.sharepoint.group.5),
33(_appstore),
100(_lpoperator),
204(_developer),
250(_analyticsusers),
395(com.apple.access_ftp),
398(com.apple.access_screensharing),
399(com.apple.access_ssh),
400(com.apple.access_remote_ae),
701(com.apple.sharepoint.group.1),
703(com.apple.sharepoint.group.3),
704(com.apple.sharepoint.group.4)