Well, naturally I think they're mainly developing the weapons that have allowed us to expel all Thargoid presence from the core of the Federation.
Well, the one thing they don't appear to be doing is that.
Aegis brought out the AX weapons pretty quick at the start of the skirmishes - surprisingly quickly, in fact, so they're probably old INRA designs that the Federation and Empire dug out of some filing cabinet - and has done nothing since. And they're not particularly effective weapons against the larger Thargoid ships, of course.
The Guardian-based weapons were Ram Tah's, who wasn't formally cooperating with Aegis until very recently.
The most recent development in AX weapons technology has been by some minor independent corporation, again not affiliated with them.
In other areas
... they set up some research stations around the Pleiades ... and managed to get most of them set on fire and unusable within a few weeks ... and then had to rely on donations to get the materials needed for repair
... they couldn't keep control over Socho, losing it to a bunch of local criminals
... they're still unable to protect any sizable ships or structures from Thargoid attack despite having had about two years now to try to scale up the field neutralisers, with ongoing deaths.
... the forces under Adm Tanner's direct authority are pretty useless
... they can't even get a basic early warning system working that doesn't require independent pilots to hack classified broadcasts
What do you think they're doing?
Honestly? I think they're there to make it look like the superpowers have an actual plan or capabilities, to avoid the mass panic that would result if people realised they didn't - same thing as The Club, just a nice fiction for the people who want to believe that there's someone competent in charge even if they disagree on ethics or objectives. Pretty much all the actual work in both research and combat areas has been done by other people.