A feature I'm building has no straightforward process or to-do list, where designs are unfinished, and designing and development go hand in hand for weeks.
We have been pushed to develop in parallel, creating much rework.
All my engineering manager asks now is ETA, even when they know it is difficult to achieve, and asks why it is late, pushing us to work late at night or on the weekends.
They do it in front of everyone or via Slack to create pressure.
What is the fundamental role of the Engineering Manager?
The specific role of the Eng Manager depends on the company, but it's a combination of delivering team impact while also sustaining/growing the engineers.
It feels like you're in an unhealthy work environment. What has the manager said when you bring this up in a 1:1? If you haven't had a 1:1 yet, ping them separately and ask to set that up. Just share your observation that asking in Slack creates pressure, and you're wondering if there's an alternate way to receive updates.
You should have that discussion with your manager, but ideally, there should be some source of truth on the status of the project. Engineers are responsible for updating the status of their work items each day, so managers and PMs have visibility on various tasks. IMO pinging people for updates should be seen as a failure of the process.