Or from the union themselves at https://www.ibew.org/media-center/Articles/23Daily/2306/230620_IBEWandPaid

We’re thankful that the Biden administration played the long game on sick days and stuck with us for months after Congress imposed our updated national agreement. Without making a big show of it, Joe Biden and members of his administration in the Transportation and Labor departments have been working continuously to get guaranteed paid sick days for all railroad workers.

Only some unions got part of what they wanted

Further on in that article,

But the unions representing workers who operate the trains day to day, such as the Brotherhood of Locomotive Engineers and Trainmen, have had far less success reaching agreement on paid sick days. “The railroads went to the non-operating crafts first and cut a deal with them,” said Mark Wallace, first vice-president of the Locomotive Engineers and Trainmen. “If a carman [who inspects and repairs railcars] has to call in sick and doesn’t come to work, the train will still run. If the engineer or conductor has to call in sick, the train is probably not going to go that day.”

Wallace said his union was negotiating with the major railroads, but said they were seeking to make it harder for the operations workers than non-operational workers to take paid sick days – perhaps by giving them demerits when they do.

The railway strike would've caused shortages of chlorine for city water supplies, shortages of essential medicines like insulin and antibiotics, severe food insecurity and inflation, and would've led to millions of people losing their jobs. Railway freight accounts for 40% of freight transport in the US. Imagine 40% of everything that's made every day suddenly not getting to where it needs to go. There's a reason Congress has never refused to block a railway strike every time it's been threatened over the last 150 years.

The contract was good for the workers but didn't include paid sick days. Congress imposed the contract on the rail workers when a couple of unions didn't ratify it (although most of the unions did).

Biden kept working behind the scenes after signing the law Congress passed to block the strike and got the rail workers their sick days without the suffering a rail strike would've had on the millions of Americans who were already struggling with high inflation on essentials. The IBEW union explicitly thanked him for it: https://www.ibew.org/media-center/Articles/23Daily/2306/230620_IBEWandPaid

By saying that he would intervene with the national guard if railway workers actually striked.

He actively pushed for, and passed, legislation that effectively forbade rail workers from picketing