So, after reading the dev blog Keeping Memories Alive | EVE Online I went thru all my research agents to complete a mission, it worked fine for all of them except one, namely Anuken Urpalen in Isaziwa, which is not offering a mission.
I had the spam as well, but it disappeared for me after I logged out and relogged. This was overnight, so I don’t know if downtime had a hand in that, but it did correct itself without help.