How can I display just the "lowest" categories assigned to an entry and not parent categories?
I could not test it, but you could try:

If you always have a Parent and 2 levels

entry.businessTypes.level('&gt;= 2').all()


If you want to only get the lowest, you could try to assign it with a condition:

{% if categories = entry.businessTypes.children %} 
    {% set categories = entry.businessTypes.level('&gt;= 2').all() %}
{% else categories = entry.businessTypes.children %} 
    {% set categories = entry.businessTypes.all() %}
{% endif %}

{% for category in categories %} ... {% endfor %}