According to this story, Arizona Democrats will hold a majority in each house of the legislature next year. The Democrats also retained the Governorship.
Democrats in the Arizona legislature were united against the 2015 law that made it extremely difficult for Libertarians to get on their own primary ballot. Democrats disliked the law so much, they have put it to a referendum, and it was temporarily repealed. But the Republican-majority simply passed it again. The Libertarian Party tried to get federal courts to invalidate the law, but did not succeed.
It seems plausible that now that Democrats will be in the majority, they may restore the old law that made it possible for Libertarians to easily run for partisan office.
The existing law is very peculiar because it only applied to the Libertarian Party, not the Green Party nor the No Labels Party in years 2024-2026. But it will apply to the No Labels Party in 2028. The Green Party has gone off the ballot because it didn’t poll as much as 5% for Governor, nor does it have registration of .667%.