How to always open links from other apps on a new tab?

Brave Search does have an option in settings that you can toggle to enable/disable this option. If enabled, when you click the link it will open in a new tab and switch to that tab.

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Edit: Ugh. Just noticed this was mobile support/android device. The above applies to desktop. I do not know if this works the same for Android devices. Leaving it for reference just in case it applies.