This is a problem that has been around for a long time. (One of the first articles I found by googling was from 1956.) It's also not specific to the US; many other countries have similar problems.
Some of the problem is very specific or localized. For example, immigration courts are chronically backlogged, and courts currently have a huge backlog because of covid.
But if we want to look at the main scope of the problem, about 57% of cases are civil, 37% criminal, and 6% juvenile. A very large percentage of the civil cases are small-money tort claims, especially personal injury suits. This suggests some kind of legal reform to cut down on the number of such cases that come to the courts. One method is to encourage mediation, but mediation tends to be unfair to individuals and favor businesses. States could pass laws that would force the loser to pay the winner's court costs, as in the UK, but this would deprive many small plaintiffs of any chance at justice, because of a fear of being financially wrecked.
Although criminal cases are only a fairly small slice of the pie, delays in criminal cases have serious consequences for defendants, who often languish in county jails. Although all 50 states have laws meant to implement the guarantee of a speedy trial as promised by the constitution, these laws generally apply only to felonies. Furthermore, the vast majority of criminal defendants are indigent, and public defenders aren't prepared to move forward that quickly with their cases, so that the laws can't be invoked.
Drug decriminalization might help, but it's hard to know. Only about 15% of inmates in state prisons are there for drug crimes. About 55% are there because they were convicted of a violent crime. Some of these acts of violence were probably committed as an outgrowth of drug prohibition, but we don't really know.
Ending mass incarceration would certainly help with the criminal backlog, but people's attitudes about how to do this are highly influenced by their political and social views. Michelle Alexander, in The New Jim Crow: Mass Incarceration in the Age of Colorblindness, says that historically, prison populations don't correlate with crime, they correlate with the building of prisons. It's possible that simply by shutting down prisons we could have a positive impact. But many conservatives dispute a lot of her claims. In general, the causes of crime and trends in crime are something that sociologists and criminologists have never been able to satisfactorily explain. There have been all kinds of theories, such as that legalizing abortion reduced crime rates, but I'm not convinced that they're strongly supported by evidence.
It would be nice if state governments could force DA's to be less aggressive in small-time drug cases. But in the United States, people vote for the DA in local elections. Typically people run for DA and for reelection based on promises to be tough on crime. The state government can't directly influence them on whether to prosecute a given case, whether to offer a plea bargain, etc.
In general, any attempt at reform will run into strong opposition from groups such as trial lawyers and prison guard unions, who have a vested interest in the status quo.