What should I do about old conversations in which I committed sins and have repented from them? Should I ask the people I previously conversed with to delete them, or is it sufficient for me to delete them from my end?

The conditions for repentance from backbiting are: regret for what has passed, immediately refraining from backbiting, and resolving not to return to it.

If the backbiting did not reach the person who was backbited, then regret and seeking forgiveness are sufficient. However, if it did reach them, or if it is impossible to reach them due to their death or distant absence, then what is required is to seek their forgiveness, or to seek forgiveness for them if that is not possible.

Regarding old mobile phone messages that contain backbiting, group members are not obliged to delete them unless it is mandatory. What you did by requesting the deletion of the conversation is sufficient, and it is advised to ignore obsessive thoughts.