The economy isn't teetering on the edge like it was in December. Also, rail is a behind-the-scenes transport mode; it gets some press, but very few people get deliveries directly by train. A rail strike in early December would destroy infrastructure deliveries right before the Christmas holiday but - unless you're in rail shipping, the average American wouldn't notice for a couple of weeks.
UPS, otoh, is very public facing operation and 11 million people receive at least one UPS package a day. That's not packages - that's individual business and personal recipients. Enough deliveries to cover every household in the US in under two weeks (that's just a reference volume: there's substantial overlap for daily business deliveries, and the delivery figure is worldwide). Every Tom, Dick, and Harriet is going lose their everloving mind if their important paperwork or Amazon packages aren't delivered. And Biden can then point to the UPS Corporation and say "hey, fellas, that's a pretty angry mob; you should do something about it," and "Republicans cut taxes on corporations so that corporations like UPS could hire more people and run more efficiently, but it looks like they're just keeping all that money for themselves." And those are much better talking points than "I'm sorry I made inflation worse and tanked the economy. Merry Christmas."
Taft-Hartley gives the president the authority to intervene in strikes if they could present a national emergency. Thanks to privatization, UPS is vital enough that it might qualify.