Is "End of engagement phase" still considered part of the engagement phase?

I am wondering about the interaction between

Petty Officer Thanisson crew : During the Activation or Engagement Phase, after an enemy ship in your at range 0-1 gains a red or orange token, if you are not stressed, you may gain 1 stress token. If you do, that ship gains 1 additional token of the type that it gained.

Captain Phasma crew : At the end of the Engagement Phase, each enemy ship at range 0-1 that is not stressed gains 1 stress token.

Seems good, not really broken by any stretch to double stress a ship and stress yourself in the process for 9 points.

Might check this post out, where this combo was discussed at length.

I think it works.

Reference!

Yes it works. At the end of a phase is still during that phase. It would be different if Phasma said AFTER the phase.