I made that mistake as a new manager by picking up a small but important task in an area I knew well. I thought it would help unblock the team, but I didn't realise I was about to go into three days of back to back meetings. After the third stand-up in a row of reporting zero progress I sheepishly reassigned the ticket to someone else, and didn't make that mistake again.

Refactors, doc fixes, low priority bug fixes, and tech debt are all fair game for managers to pick up. I do think it's important to keep your hand in.