We flew SAN/LHR/BER a couple of weeks ago, booked as an AA codeshare. I have the Citibank Executive Mastercard that includes Admiral's Club access. Both of our flights were in T5. I was unable to gain access to the BA lounge using this card. (It worked during the pandemic when AA shut down their club.)

My question is - having cleared security to get into T5, if we had taken the shuttle over to T3, would we have to re-do security? Also upon returning to T5? It didn't seem worth the hassle to me so we just found a place to crash.

On our return flight both segments were in T3, which worked out fine.