Works exactly as I hoped it would!

Only thing to note is that clicking the button that can be added to your add-on bar instantly performs the function of opening the tabs in your clipboard (as opposed to opening any kind of menu or dropdown, which is what I'm used to) - generally not a problem as this is what the extension is for, but just beware for the first time/if you accidentally click it when having a ton of links in your clipboard!

Works.

Does the job, but has 1 problem - if clipboard contains text without links, it ignores it instead of searching for it (which is the desired behavior, exactly as address bar works)

Edit: Also, a bug (solved, see Edit2): first it opens tabs properly to the right of current tab, then it rearranges them in the opposite order, placing them to the right of the tab that's to the right of one where you were. That is,
you have tabs "a B c d" with B being selected
you open links "1 2 3" and end up with "a b c 3 2 1 d"
This must be because the extension doesn't account for browser.tabs.insertAfterCurrent = true

Edit2: The bug was caused by Open Tabs Next to Current extension. Nevermind. That one doesn't do its job very reliably anyway.