Assembly machine to asssembly machine (lvl2)
Assembly machine to lab
Currently I keep having to manually intervene as the inserters don't do anything. Did I miss a trick?

An assembler won't input things it doesn't consume. And won't output things it consumes. But it's hard to tell what the assemblers are actually set to
The problem with this setup is that Automation and Logistic science packs are both on the same side of the belt so the inserter can only ever grab one or the other. The research requires both so the lab will not start consuming science packs until at least one of each is in it's inventory. The lab already has some Automation science packs in it so the inserter will not load another into it, never getting the chance to insert a Logitic science pack.