Filter gallery by comparing Choice column options from a List, against the items in a collection

I would advise against using multi-choice columns as they are not a valid concept in relational databases (a multi-choice field is not an atomic value and so violates first normal form) and so cause lots of problems for querying, as your question demonstrates.

Others here may be able to suggest some tricks/work-arounds, but I would suggest modifying your data structure to avoid the use of multi-choice fields.

Note that SharePoint is very limited as a datasource in terms of relational querying ability (probably why it implemented choice fields in the first place!), so consider how much data your App will need to hold/manipulate and maybe consider a different datasource (though this will have licensing implications, so you may need to also consider a platform other than Power Apps as well).