Discussing something like this can not be boiled down to a distro choice. It is a larger design problem.
The following is my idealistic vision of how the problem could be approached.
Let’s say a regional administration, like a city or municipality, decided to switch to Linux, staying away from Google and Microsoft as much as possible without entirely sacrificing usability and familiarity. This would include self-hosting various things expected to be available in the world of office jobs. Email, cloud storage, calendars, etc.
For the average end user, such as a worker doing office tasks, you would deploy workstations with a preconfigured desktop environment.
This configuration would need to be consistent across the organization - allowing for peer tech support for simple problems - but still include appropriate granular modifications for different departments, to accommodate for any department-specific, specialized needs.
The end users - the office workers - would form the base user group. The base users are not, under any circumstances, expected or assumed to know much about Linux or computers beyond the GUI paradigm and whatever software their work requires. The OS and DE should either stay out of the way or genuinely assist the user.
Then there would be the intermediate user group, eg. support staff. The people who configure and deploy the workstations and come to the rescue when something breaks or does not work as intended. They would also be there to guide in the initial transition.
These people would receive a vocational training, including Linux basics, a familiarization with how to configure and troubleshoot whatever distro is being used, and hardware maintenance.
They would have access to a service manual, an internal wiki providing documentation and guidelines up to a point where it becomes a problem for the next group.
Finally there would be the advanced user group, the IT administration. Workers in this group would be responsible for hosting services, network infrastructure, choosing the hardware, backups, etc.
In addition, they would maintain the service manual and manage the intermediate staff.
They would also be in direct contact with the the distribution maintainers, to prevent and solve any deep-rooted problems.
Extensive Linux experience is expected.
Note that while language about such hierarchy may sound oppressive, I don’t mean to say that one group is better than the other.
The hierarchy is there to demonstrate the fact that not all people are interested in learning Linux in addition of doing their own, actual job that they have an education for, and that is perfectly fine.
I see it as an opportunity to easily and fairly employ more people in the public sector, providing work also in regions with high unemployment.
Even the intermediate group can be a tempting offer if the pay is good and education is readily available.
There would also be internal career paths from intermediate to advanced for those who are interested. Apprenticeship contracts, subsidized internships, etc.
Now, the distribution itself.
It should be something tailored for the public sector specifically.
It should be mass-deployable, obviously.
Also, remote support and maintenance should be possible.
It should emphasize security and stability but also keep up with usability improvements for the DE and any software.
The graphical user interfaces should be translated and localized with utmost care.
There should be a fork of the distribution running on workplace-issued smartphones, allowing for seamless integration with the workstations and the ecosystem.
Ideally this kind of distribution would be devloped and maintained by a nationwide (or EU-wide) institution, such as a politically independent foundation. The foundation and its rules would have to be carefully crafted so that authoritarian political forces could not defund it or take it over.
Finally, the development work should be partly guided by something like a council or an advisory board consisting of members from all three user groups.
I have no idea if something like this could exist or function in today’s world, but one can always dream.
Employing people might be cheaper in the long run than setting up data centers etc…