@leocg Hello again. The fact that it worked partially told my guts feeling that there isn't s.th. well implemented at my end. Therefore i entirely removed the agent-switcher extension, cleared caches, restarted the browser, reenabled the agent-switcher, and bang: now it works consistently across all webpages i tested so far. So the agent-switcher still is a proper workaround.
Still it would be great, to make this choice an option of the browser, be it in it's configuration or as a "save" panel option.
But thank you very much for your quick response and willing to help!