The EPIC Time Conversion and Manipulation Thread!

I think this is what you’re looking for:

{% set last_changed = states.binary_sensor.main_door.last_changed %}
{% if last_changed < today_at() - timedelta(days=6) %}
  More than a week ago
{% elif last_changed < today_at() - timedelta(days=1) %}
  {{ last_changed.strftime('%A at %H:%M') }}
{% elif last_changed < today_at() %}
  {{ last_changed.strftime('Yesterday at %H:%M') }}
{% else %}
  {{ last_changed.strftime('Today at %H:%M') }} ({{ relative_time(last_changed) }} ago)
{% endif %}