My coworker keeps taking credit for my work in meetings and my manager still thinks he's the one doing everything

I work on a small team and for the last four months I've been the one actually finishing the reports, fixing the spreadsheets and staying late when something breaks. My coworker "helps" by sitting in the same Slack channel and then restarting my updates in the weekly meeting like they were his idea. Last week he even used a slide I made and didn't mention me. I tried documenting everything in email so there's a paper trail and I brought it up once in a 1:1. My manager said we're a "collaborative team" and I should be less territorial. Now I'm starting to look pretty if I keep correcting him in public, but if I stay quiet he keeps getting praised for work I did. I don't want to blow up the team, I just want the credit to land on the person who actually did the thing.