Of course for Primary Campaign, we have the field "Opportunity.Campaign", which is a lookup(Campaign) field on Opportunity. But there is also a related list for the Opportunity record detail page called "Campaign Influence", which can be populated in a couple of ways, including manual button-click to "Add" an Opportunity Campaign Influence record. This appears to be like a many-to-many relationship, implying that any opportunity can be linked to any campaign, non-exclusively so. That seems to imply a junction object.

I suspected something like OpportunityCampaign or something, but no such object exists.

Where are these relationships stored? How can they be created/modified via API or Apex (or even workflow)?