There is a setting in System Preferences > Dock called "Prefer tabs when opening documents". Change this to "Manually", it's probably set to "Full Screen Only" mode right now.
Not sure why this setting is under the Dock preferences but this will fix your issue. Downside is I think all applications behave that way now, like Finder and Preview. I guess you can't pick and choose specifically how you want an app to behave.
I turned it off because I am trained to use Cmd+N for new windows, and Cmd+T for tabs. It makes little sense why Cmd+N and Cmd+T would both open tabs regardless of settings. Why have the command execute from 2 different keyboard shortcuts, especially by wasting a classic shortcut that many have engrained in their heads.
Answer from am_water on Stack Overflowmacos - "New Window" keyboard shortcut in Safari - Stack Overflow
shortcut - How to make ⌘N open a new window in Safari? - Ask Different
open link in new tab - safari shortcut
macos - Shortcut for making a new window in Safari - Ask Different
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There is a setting in System Preferences > Dock called "Prefer tabs when opening documents". Change this to "Manually", it's probably set to "Full Screen Only" mode right now.
Not sure why this setting is under the Dock preferences but this will fix your issue. Downside is I think all applications behave that way now, like Finder and Preview. I guess you can't pick and choose specifically how you want an app to behave.
I turned it off because I am trained to use Cmd+N for new windows, and Cmd+T for tabs. It makes little sense why Cmd+N and Cmd+T would both open tabs regardless of settings. Why have the command execute from 2 different keyboard shortcuts, especially by wasting a classic shortcut that many have engrained in their heads.
I've discovered if you set "New Tab" as ⌘N and "New Window" as ⌘T it will work, ⌘T will open a new window and ⌘N will open a new tab, even though that is backwards, if you switch them to the right way, they both just open a new tab. Annoying, I know.
In System Preferences > Dock if Prefer tabs when opening documents: is set to Always that will cause a tab to open instead of a new window.
Changing it to Never will allow ⌘N to open in a new window.
There is also an In Full Screen Only option.
Basically user3439894s answer but on macOS BigSur, the option is located in System Preferences -> General menu.
Knowing now that there is a menu entry "New Tab at End", there is no need for an Apple script or QuickSilver or anything. Just open System Preferences > Keyboard > Shortcuts, and add a shortcut using the plus button like the following:
I believe while in Safari, using the keyboard shortcut ⌥ ⌘ T Will open a new tab to the far right
tell application "Safari" to activate
tell application "System Events" to tell process "Safari"
keystroke "t" using {option down, command down}
end tell