Hence it is very important for everyone to share the status of what they are working on along with any dependencies and challenges they are facing with everyone else. Any changes to the task timelines also need to be communicated so that everyone is on the same page. Over time you will notice members of the team getting comfortable and candid in their status as long as an open communication without prejudice is maintained.
It is also very important to respond as soon as it is done to inform everyone else that it is done. Do not wait until the end of the day to inform other members of the team. This way it becomes clear to all the progress being made in the project.
Some teams maintain shared excel sheets, others use tools like Trello, Microsoft Teams, Bitrix, etc. What ever it is, encourage all to update it freely and openly.
Do not ever try to get everyone to send the status to one person, that person filters, collates and then distributes it. This will give you the status of the tasks through the lens of one person, which need not necessarily be the exact status of the project depending on the persons view of the project.