I doubt that there is a direct way to do that. What you can do is right-click a link and select "Open Link in New Tab". There are also preferences you can set to direct that links are opened in a new tab. See, e.g, https://support.mozilla.org/en-US/questions/1365765#answer-1477990

Everytime I try to detach tab into separate window, it almost instantly get clogged by new links, whilst I really want it to be 'as is' with selected tab (single tab) been visible all the time and not put to background by every new link I click in the external messenger.

Are they links from other applications being sent to the "last active" window?

How can I move tab into separate window and 'block' this window from been used for new links?

In theory, at least, you could launch the page as a new popup window instead of moving the tab to a new regular window. The trick is to specify certain features such as height and width that trigger a special purpose (dialog-style) window. If you try to open a new tab in that kind of window, it will open in the last active regular window instead. If you want to see an example of this, use the third link on the following test page:

https://www.jeffersonscher.com/res/popit.html

Whether there is an add-on for that, I don't know. You might need to roll your own -- for example, using a bookmarklet. I posted one here if you want to try it: https://www.jeffersonscher.com/res/sumomarklets.html#popthis