Superman is actually a trademark and its always been held by DC. Technically Clark Kent and Lois Lane are trademarks held by DC as well. Technically you can use a trademarked term as much as you'd like in a product, you just can't use the term in your promotional material (i.e. you could have characters in a story talking about Superman for the entire length of the story and no violate the trademark if you never mention "Superman" as part of promoting the story).
Where it gets messy is the copyrighted concepts also make use of those terms. In this case, if DC lost access to the AC1 copyright, they could still technically use the Superman, Clark Kent and Lois Lane trademarks, but they would not be able to use them in the combinations that were used for Action Comics #1. So you could have a Superman, but he couldn't be Clark Kent and Clark Kent couldn't be a reporter or in a relationship with Lois Lane who also could not be a reporter.
What you COULD do though is introduce Superman who is actually time-refugee Clark Smith (for purposes of copyright and trademark these things can get ridiculously specific) and married to fellow time-refugee Lois Smith who is an author.
Then, because trademarks are "use them or lose them" in nature you just need to find ways to periodically maintain the Clark Kent and Lois Lane trademarks. Not maintaining the trademark is how Marvel has "Captain Marvel" but the original Captain Marvel has to be called "Shazam." DC lost it through lack of use and Marvel snatched it up. This would be particularly important if they lost access to AC1 (or it finally entered the public domain) so they could prevent a series called something like "a.k.a. Clark Kent" or "The Adventures of Lois Lane" to be published.
One way they might do that is to create a new Clark Kent character to use the name... say a completely human reporter whom people once mistook for Superman. Similarly, you might keep the Lois Lane name in play by making it a pseudonym that the author Lois Smith employs for her novels.
The thing about movies and, to a lesser extent, television is that they are much more fixed points in time. You only have to be worried about the state of the copyright at the time you produce the product. You don't have to destroy the film just because the copyright later lapses. So they can make use of the copyrighted material until they can't without as many problems.
You could technically do the same thing with the comics as well, but due to the extensive continuity the audience prefers, having to completely retool stories that might be presently relying heavily on the copyrighted elements would be a much bigger pain than simply pulling a reboot on a the movie franchise.
Supergirl is owned entirely by DC so she's not a problem at all. Her being Superman's cousin would not need to be affected by any changes to Superman himself. Heck, there's a strong likelihood that the reason they decided on a Supergirl TV series over adding a new Superman series to the Flarrowverse was because they DO own her lock, stock and barrel while a successful Superman series would be another invitation for another lawsuit as some lawyer decides the heirs aren't getting enough of a cut (ex. a young Superman at the start of his career finally going public now that all these metahumans have started popping up would have worked without needing to have the series be in a separate universe).
IF something were to ever happen to the AC1 copyrights they could just keep the story focused on Supergirl and maybe make some reference to Superman and Lois having to abandon their lives as Clark Kent and Lois Lane because Lex Luthor learned Superman's true identity and them sticking around put the people around them at too much risk (if they wanted a comic reference they could let Kara know that they're now going by Mr. and Mrs. Smith).
As to Krypton; Krypton and the name Kal-El are actually fully owned by DC because neither appeared in Action Comics #1 (which is the ONLY part of Superman in dispute). The dying planet was unnamed and the character was only called Clark Kent and Superman... never Kal-L (or Kal-El). All they'd need to do to keep Krypton in play is make sure that its death was not due to "old age" (the copyrighted element) and make it say, due to Brainiac's tampering with the planet's core, and downplay the part where Superman was rocketed away from it as an infant.
Jonathan and Martha Kent weren't part of AC1 either, so they can be referenced without issue. The same for Perry, Jimmy, Lex Luthor, Kryptonite and the Daily Planet.
It really does. Heck, I think Superlad93 or someone even created the opening blurb for a Flarrowverse show based on the concept at some point and it was much more straightforward than you'd think based on all the problems the people who need the timelines merged keep expressing. It even had the notion of "I lived a normal life but then X happened and I had to take action" built right into it.
The sheer pop-culture inertia of Superman actually really works to DC's favor if they wanted to stop referencing AC1 as part of a new production. The basic origin story is so well known that re-telling it straight is practically a waste of time in terms of a narrative (which is why every time its retold these days there's usually some major twist or another to it... "we're putting the McGuffin into his cells to keep it away from Zod" or "His cousin was actually sent along with him but got knocked off course").
But with the "time refugees" you could start the story at the point where Superman and Lois are losing their world and escape to a new one. Heck, you could even get very meta with the whole thing if you wanted to put it into a new medium by actually aping the traditional Superman origin by at first making it look like its Jor-El and Lara about to send their infant son away... only instead its Clark and Lois with their infant son at the Fortress and they're preparing to open a portal to escape because their universe is collapsing.
Heck, make it the Tesseract version of the Fortress they were visiting and the universe has already collapsed (i.e. Superman isn't leaving anyone behind) and they only have a short time before the Fortress collapses too (maybe they were at the Fortress because they wanted tech and robots familiar with Kryptonian physiology present for the birth of their son).
The point being, you can make the whole concept extremely familiar (fleeing a dying world using Kryptonian technology) but turn it to a completely fresh story where Superman and Lois have to start their lives over in a new world (echoing the stories of refugees who have to flee their homes as adults and try to rebuild elsewhere).