They actually flip flop a lot.
2006: Migration to LiMux begins
2008: 1200 out of 14,000 have migrated to the LiMux environment
2013: Over 15,000 LiMux PC-workstations (of about 18,000 workstations)
2016: Microsoft moves german HQ to Münich
2017: Dumping Linux https://www.linuxinsider.com/story/munich-city-government-to-dump-linux-desktop-84307.html
2020: Going back to Linux https://www.zdnet.com/article/linux-not-windows-why-munich-is-shifting-back-from-microsoft-to-open-source-again/
2023: Microsoft opens new Experience Center in Münich https://www.munich-business.eu/meldungen/neues-microsoft-experience-center-emea.html
2023: Analysing what needs to be done to switch to Win10 before new vote https://www.tweaksforgeeks.com/ditching-linux-for-windows-after-wannacry-is-too-risky-for-munich-green-party-warns/

The switch back to Windows was not because of vad productivity. They switched back when the new Major got a visit from the microsoft CEO.

https://www.heise.de/news/Endgueltiges-Aus-fuer-LiMux-Muenchener-Stadtrat-setzt-den-Pinguin-vor-die-Tuer-3900439.html

https://www.sueddeutsche.de/muenchen/muenchen-microsoft-linux-verwaltung-1.5562006?reduced=true

The problem with that is a few years is a bit short to get real benefits out of it. And the Wikipedia article contradicts the statement that productivity went down. Actually issues and errors went down, half the workforce was alright with it and they saved tens of millions of Euros. And then they cancelled it. That decision wasn't backed by technical or factual reasons at all. Many people said they were fine with Linux. Issues were for example that they had old and outdated computers. As a reason to switch back they claimed: sync to mobile phones had issues (...as if government workforce syncs their calendar to their mobile phones...) and these were issues with the groupware suite. Nothing had anything to do with Linux, productivity or the people who sat in front of the computers and actually had to use it. There were quite some benefits and from the technical side things were going well despite admins not being backed by their superiors and the city. They did a final study which contains quite some / mostly dubious statements, and Microsoft also was involved in the switching back.

You CAN enforce a change. Sure, change is always hard in the beginning. But we do it all the time. The story of LiMux is more: You can destroy anything if you really want to. And politics likes to twist things so it suites their narrative. (And lobbyism is a thing and Microsoft is better at it than the Linux community.)

Sounds like very poor management since everytime a business company switches system infrastructure, the end-users will receive courses. I was working in a factory which changed the automation system and every end-user spent 4+4 hrs in the lecture room and after 1 month of use they had again 4 hrs advanced use cases lecture.

After just 6 months every worker said the new system is easier and better, which first seemed to be impossible transfer.

How did they measure productivity of a city administration? !?

Interesting!

From my experience as an executive I recon they haven‘t factored in the side effects like vendor lock-in, customizability and application speed of changes. Those are pretty hefty sums over years/decades.

When you don't know something, it's completely ok to not say anything.