To show other collection members on your product page, you can use product.collections to return an array of the collections that the product belongs to. From there, you will probably just want to return the first collection in that array:
{% assign product_collection = product.collections.first %}
{% if product_collection %}
This product is part of my {{ product_collection.title | link_to: product_collection.url }} Collection
{% endif %}
Or you can change the first line to include the handle of your “Collections” linklist:
{% assign custom_collection_linklist = 'all-collections' %}
{% assign product_collections = product.collections | map:'handle' %}
{% for link in linklists[custom_collection_linklist].links %}
{% if link.type == 'collection_link' and product_collections contains link.object.handle %}
{% assign product_collection = link.object %}
{% break %}
{% endif %}
{% endfor %}
{% if product_collection %}
This product is part of my {{ product_collection.title | link_to: product_collection.url }} Collection
{% endif %}
I hope this answer helps. If you feel like my answer is helpful, please mark it as a SOLUTION