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There are a couple of unrelated issues potentially being raised. One is basic economy fare restrictions, and the other is what benefits your Silver status confers (which will apply for all future flights as soon as you qualify).

The bolded word with parenthetical is just being used as a catchall for the fact that when TATL Light/Basic fares were introduced, not all the *A partners used the same verbiage for the fares.

It doesn't appear that you've purchased such a fare, but just to be certain, are you able to make some seat selection (even if restricted options) for your EWR-BCN flight? If so, then you do not have a Basic Economy fare, and you are eligible to apply for a cabin upgrade. You can also check your fare rules to see if the code ends in LGT (meaning Light/Basic), which would preclude an upgrade.

Note that if you want to upgrade to Business, you will need to support the upgrade with miles from your account or pluspoints gifted by someone. There are no complementary upgrades for long haul international flights. If the upgrade request is waitlisted, your status will help with priority a little bit, but otherwise there is no requirement to have status for requesting an upgrade to Business.

With your silver status, you will be eligible to select an economy plus seat at check-in time for yourself and partner with no charge.