Because we need different widgets in the sidebar on every single page I had to install a plugin to exchange the default sidebar…
unfortunately there is no option to sync the one widget to the needed pages.
Is there any possibility to sync widgets with coding?
Which sidebar plugin are you using? I assume its creating new sidebar areas that you conditionally display.
There are other plugins such as Conditional Widgets and Dynamic Widgets that allow you to set the conditions at the widget level, so one sidebar for all areas that display dynamic content.
The alternative would be to create a shortcode to output your content. Let me know.