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Explained: Why you can't move Windows 11 taskbar like Windows 10, according to Microsoft
(www.windowslatest.com)
This is a most excellent place for technology news and articles.
Yes! I'm not sure about it changing when you connect monitors (since I'm usually using desktop PCs), but you can have a different setup per monitor.
I have three monitors at work. My main monitor is configured to show all open apps in the taskbar, while the secondary monitors only show the apps opened on those monitors. You can totally change any of the configuration though... the layout, the position, the settings, or even just not have a taskbar on some monitors.