Fix task filtering and completion persistence

[pablodcruz]

Summary

• fix status filtering to use the requested status value
• add case-insensitive task search across title and description
• persist completed task state and completion timestamps

Verification

• ran the documented lab verification flow against isolated task data
• confirmed status and combined search filters return the expected tasks
• confirmed completed tasks remain done on a follow-up read
• confirmed the working tree remains clean with no runtime data churn