Gosh, coming here for advice is an invidious exercise.

Giving examples of another carrier being willing at some point in the distant past to interline bags onto a BA service is hardly helpful. The advice about bmi was just wrong.

The facts are:

BA doesn't interline bags to a non-OneWorld carrier unless (a) it is on a single ticket; or (b) the agent doesn't know the rules.

BD doesn't interline bags unless (a) it is on a single ticket; or (b) the agent doesn't know the rules.

It is not wise in either of these examples to bank on (b).

Whether TAP adpots the laissez-faire attitude of some of the US carriers we have not yet established (and as G-BOAC rightly says, that's really a question for another board). Can the OP insist that TAP interlines the bags on two separate tickets? AFAIK, no.

Hence, the only safe piece of advice - pending clarification of TAP's tolerance for interlining baggage - is assume that they won't.