I've been quite vocal regarding my liking of the new systems in place for official factions over various discord conversations, and this hasn't changed after the first quarter came to a pass.
Back when the OF changes were first announced I was a bit skeptical. It has been too many years in Discovery where being in an OF didn't really mean you have any actual benefits over anyone flying indie IDs, while having multitude times the responsibilities. I have to admit, though, that the staff did an insane job reworking official factions. The various crazy new rights we have access to, as well as being included in story development matters and being given the freedom to effect story outcomes - to a degree - is something that I never thought would return to Discovery. You basically found a way to reintroduce the Discovery Working Group (I think that's what the server was called?) in a way much better than its original implementation, and for that I must commend you.
All those general comments aside, now to reply to your questions;
1) Is the current system an improvement? Yes, it absolutely is. Official factions actually feel meaningful now both in terms of gameplay (via access to various new game-changing faction rights) and in terms of roleplay (via discussing story developments).
2) Are the requirements proportionate? That's a difficult one, as it always is when it comes to activity. Is 2 days for a whole faction + 3 members that logged a measly 3 hours per quarter proportionate to the power official factions have? No, not really. You'd need to bump up those requirements a lot if you wanted them to match the benefits, and the reason I was skeptical at first is because I thought the staff would do exactly that. This isn't a matter about the requirements being proportionate or not, it's a matter of the requirements being logical in a community such as Discovery's in 2026. You did an amazing job to introduce requirements that don't feel grind-y and aren't annoying to fulfill.
3) Are the quarterly faction reports useful to the wider community? You introduced an idea to me that I hadn't thought of beforehand, when you posted on the main discord server and linked the reports thread, telling people to read it as advertisement for official factions. The report system became so much more genius to me when I realized that it's not only for staff to "judge" who is worthy of official status and who isn't, but it also effectively is people advertising their factions to the community. A new player can very easily navigate to that thread, read the information + goals + future plans of factions and decide what they want to join, without wondering what the future agenda of the faction is. Peak Jammi, rated 11/10.
4) Are there areas for improvement, and if so how? The only thing that comes to mind is the part about the active leader being a requirement, but as long as there is at least one person willing to step up - even if temporarily, as you noted on a reply of yours above - it will never become a problem. Sure it probably is a tiny inconvenience, as it was for us in 46th to have to swap leadership from Doc' who has carried us for so long, but it /did/ lead to the faction suddenly becoming alive and participating in server developments. I can't say it's negative change, after all.