Seems like the franchise is safe just a bunch of executives at some subsidiary squandered everything.
"Gainax tried to rebuild itself with the support of Khara, which currently owns the rights to the Evangelion series and of which Anno serves as president."
So all the actual franchise stuff was with Anno in Khara, and Gainax was the creative staffing for the anime/movies?
Khara and Trigger are the successor studios to Gainax as in that those are the studios made by their biggest creatives, and it's to my understanding that all relevant IPs from the creatives behind Khara and Trigger during their time at Gainax were transferred to them after the buyout. The only Gainax IP that's not owned by the creative behind it is FLCL, since Gainax sold the rights for it to Production I.G. in the late 2000s.
Another, more indirect, successor studio to Gainax is Studio Cloverworks at A1 Productions, although that one was mostly general staff.
That said, it's not like Gainax did much in the ~5 years between the formation of Studio Trigger and the buyout; they released exactly one anime and one OVA. There was pretty much nobody creative left at the company to make anything, specifically because the CEO got cold feet on approving creative projects.
All the valuable assets are going to the people who matter: Cloverworks, Trigger and Khara. Its a bit sad for Gainax as an entity to be collapsing, but the individuals who bring us these stories (through producing, acting, animating, or other skills) still exist out there.
I'll definitely say that Evangelion 3.0 + 1.0 from Studio Khara lost a lot of the mech-design that made Gainax great... but its clear that all the "mech designers" are alive and active over at Studio Trigger.
Its sad to see the team split up, because nothing like Evangelion (90s) will ever come out again. But on the other hand, these other studios are clearly active and seemingly successful. So the show goes on...
One small correction though: no IPs will be transferred to Cloverworks as far as I know. Cloverworks didn't really get any specific creatives from Gainax, moreso just that a lot of the intermediate staff that you usually don't hear about ended up at Cloverworks. (Which to my understanding was largely a coincidence: A1 had formed Cloverworks, put out hiring ads and in the next month, Gainax basically declared they weren't ever going to make any experimental anime again, causing a mass exodus from the company.)