As I recall, you have these tables/relationships:
Where in these tables do you record the Edition? is there a field for that in Surveys?
Yes. "Edition" is a field in Surveys.
Then if you went to a layout based on Join _Issues_Assigned, you could perform a find that specifies one or more Editions in fields in the related Surveys table. This will find all Join table records that are linked to a survey record for the specified Edition(s).
The other criteria: Surveys that have at least on Issue Assigned
Is handled automatically as you won't have a join table record unless there is an assigned issue linked to that survey record.
Since your layout is already based on this join table, you thus have produced the needed report just by performing a find followed by sorting your records into the desired sort order.