AITA for emotionally moving on before my relationship officially ended?

I was in a relationship with my girlfriend, let's name her Emily. A little before I left on a business trip, our relationship had already started falling apart because of a complicated issue that kept causing arguments. I felt emotionally trapped, and over time I realized my feelings for her were fading.

While I was away on the trip, I met another girl, let's name her Sophie. We spent a lot of time together and gradually became close. At some point, I realized I had developed strong feelings for her. At that time, I was still officially dating Emily, but emotionally I had already checked out of the relationship.

I never confessed my feelings to Sophie while I was still with Emily, never flirted in a way that crossed into an official relationship, and never told Emily there was someone else. I knew that starting a new relationship before ending the old one would have been cheating, so I waited.

A little later, Emily texted me saying she didn't think we were right for each other anymore and that we should break up. I calmly agreed because I already felt the relationship had reached its end. There was no fight, no blocking, no insults we simply agreed to stay following each other on social media but never contact each other again.

Only after the breakup did, Sophie and I officially start dating. She knows the entire story, as do my close friends. Emily has no idea that my feelings for Sophie had started before we officially broke up.

Looking back, I know this probably wasn't the most honorable way to handle things. I couldn't control developing feelings for someone else, but I probably could have been more honest and ended the relationship myself instead of waiting for Emily to do it.

So, AITA?