Homework feedback is the part of the week that stretches. You already know what the student missed. Writing it down again after the lesson is what eats the evening.
The useful split is simple: something else can gather the submission and sketch a first pass. You still decide what goes out.
Keep the first pass a draft
Bomi reads the file against the assignment and drafts a response: what worked, where the method broke, what to practise next. You edit it. Nobody else sees it until you say so.
That is the product. Not autonomous grading, and not a replacement teacher. The draft saves the blank page. The judgement stays with you.
End with one next step
A mark without a next action just sits there. The stronger note says what to retry, in one sentence.
For one student that is a short method drill. For another it is the same explanation in the family's language. Keep it short enough that you will actually send it.
Parents need the week, not the markup
Parents do not need every red mark. They need: this is what we reviewed, this is where it is getting steadier, this is what we do before the next session.
If that summary lives next to the homework, instead of in a separate email you write from memory, it actually goes out.
Small enough to repeat
If the loop only works on a quiet Sunday, it will not last. Collect the work, review the draft, send one next step. That is the whole system.
The version worth keeping still sounds like your tutoring. It just gives the admin somewhere to go.