This fall, I'll be a reader (i.e. homework grader) for the first time, and the course is a second-level linear algebra course, which is likely the first proof-based course most of the students will experience. Most students will be in a math major (more applied than pure) but some will be from other STEM areas. Points will be awarded based on rubrics, but I feel like additional feedback is especially important and formative for a first proof course.
Unlike grading as a TA, I won't be able to communicate with students outside of writing notes on their solutions, and students will not be allowed to contact me directly (they must go through the TA to ask for regrade requests, etc.). If I could talk the students, I'd be able to get their feedback and adjust as I go, but this will not be possible for me as a reader. What are some general best practices for grading and giving feedback in a way that lets students have a good experience?