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There is a setting in "Settings -> General -> Tabs" to divert a link that specifies a target window in a new tab. For links that do not specify a target window (i.e. open in the current tab), you need to use the context menu or hold the Ctrl key and left-click or middle-click the link with the mouse wheel. You can search the Add-ons website for a suitable extension.

Example of an add-on you can set to send ALL links to a new tab, or only different-site links:

https://addons.mozilla.org/firefox/addon/open-link-with-new-tab/

Note that you do need to configure it to notice any change, and some sites may work around it.