Add lockable student placements for random assign, bench all, and solve

[Peaj]

Summary

Add a way to lock individual student placements by clicking on a seated student, so teachers can keep selected students fixed while updating the rest of the seating plan.

Problem

Teachers often want to keep a few placements they are happy with and only reshuffle or re-solve the remaining students. Right now Random Assign, Bench All, and Solve Plan treat all students the same.

Desired behavior

• Clicking a seated student should toggle a locked state for that placement.
• A locked student stays in that exact seat when using Random Assign.
• A locked student stays in that exact seat when using Solve Plan.
• Bench All should leave locked students seated and only bench unlocked students.
• Unlocked students should continue to move around the locked students normally.

Suggested implementation

• Add a visible locked/unlocked state to seated student chips.
• Persist locked placements in project/roster state so they survive reloads and exports.
• Treat locked placements as fixed assignments when randomizing or solving.
• Prevent benching/removing a locked student unless they are explicitly unlocked first.

Acceptance criteria

• Teachers can lock and unlock seated students directly from the grid.
• Locked students remain fixed during Random Assign, Bench All, and Solve Plan.
• Solver statistics and resulting assignments still update correctly for the remaining unlocked students.
• Locked state is preserved across save/load and local persistence.
• The UI clearly communicates which students are locked.

Notes

This should support the workflow of manually fixing a few placements first and then optimizing the rest of the class around them.