Why did Serini keep the diary:

Serini was young and naive when she joined the Scribblers. She starts a diary of her first adventure, not realizing how important and dangerous the information she was recording would be.

Later, the group tells her to write down the coordinates of the Gates in code. Still being naive, she writes them down in her diary alongside her other not secure secrets.

After building her dungeon and deciding to return to adventuring, she probably knows a bit more about security. More important though she loves her friends. So despite the risks she keeps her diary with her as a memento of the good times they had together.