Sort notifications by their purpose
Notice which notifications require an action and which simply suggest content. Begin with one application and review its settings rather than changing everything at once. Check how important people and services reach you before broadly muting alerts. Do not alter a system used for individual health or safety on the basis of a general decluttering idea. Keep decisions specific to the device and circumstances you understand.
Agree on expectations about replies
Discuss whether every family-group message needs an immediate reply. It can help to distinguish a changed arrangement from an ordinary photo update. Agree separately how the people concerned should communicate in an urgent situation. Do not treat an icon or silence status in a chat group as a reliable emergency communication system. Revisit expectations if the arrangement creates more confusion than it removes.
Your next little step
Choose one idea that suits your family and try it at your own pace. Every family has different needs.
An example in practice
You could begin by reviewing promotional alerts from one shopping application. Then explain to your family group that you read ordinary updates when you are available. Check on your own device that the important contacts you intend to keep can still reach you.