WARNING: The following contains spoilers for takt op.Destiny Episode 7, "Truth -Noise-," now streaming on Crunchyroll.
Cosette's death in takt op.Destiny had a heavy toll on Takt and Anna. Anna lost a sister and Takt lost someone who he held as close to his heart as he did music. After Cosette reawakened as a Musicart, it appeared as though things were back to normal: Takt and Cosette still bicker and Anna is often the mediator during these instances, but there's a noticeable awkwardness between the three. Things have changed and none of them are really sure what to do about it.
Since reawakening, Cosette has insisted that her new name is Destiny, but Takt and Anna have yet to start using it. If they do, it might mean they have no hope of bringing her back, which is why the New York trip is a bit of a Hail Mary for them. However, as the audience has seen in the recent episodes, Cosette's humanity is returning little by little.
As a thank you for his performance, Takt is gifted sheaves of blank composition paper. Although he's a talented and proficient pianist, composing music is an entirely different story. He spends every single second poring over the paper, fingers drumming out an indiscernible melody that nobody can hear except for him, but nothing is flowing right. Takt is still struggling to cope with Cosette's passing, as symbolized through his composition process. He's stuck both literally and figuratively in this strange in-between: if he accepts her passing, he'll have to admit that she's truly gone. He's not sure what kinds of emotions he wants his piece to convey.
As he learned in Episode 6, music is the vessel for people's feelings. It's a record of people's histories -- and it's a way for Takt to finally express all of his emotions: his love, guilt and grief for Cosette. It also explains why the title of the anime is takt op.Destiny. The 'op' in the anime's title is short for 'opus,' which is used to help categorize and organize music. takt op.Destiny alludes to Takt's eventual finished work.
Anna and Takt are both going through stages of grief. In the earlier episodes, Anna was still desperately holding onto the hope that the old Cosette was still somewhere in there, but in Episode 7, she seems to have moved on to the acceptance stage, resigned to the fact that this Cosette isn't her sister. She can't yet call her Destiny, but she has stopped calling her Cosette.
The ironic thing is that both Anna and Takt are trying in their own ways to move on, but Destiny is slowly embracing more and more of her humanity. She is visibly worried when she sees how exhausted Takt looks, and she tries to support him as best as she can by not bothering him when D2s attack and by finding him a melodica to help him compose.
She's not Cosette, but she's not not Cosette either -- there are still remnants of the old her, as Episode 7 proves. The one person whom Takt wants to hear his music and whom he composes a piece for is no longer alive. His piece is both his love song and his goodbye to Cosette, and it most likely symbolizes Takt's reconciliation of her death, which might explain why the anime title says Destiny rather than Cosette. Destiny may not be the Cosette who Takt once loved, but that doesn't mean she's gone forever: she's just a different Cosette.