Psaki (and the media) are damned liars!
Trump announced at a rally he'd already made his pick to replace Ginsberg. He simply made it public early that his nominee WAS IN FACT a woman without announce WHICH woman he'd picked.
He by no means promised to nominate a woman before making his selection -- unlike Biden who made it a campaign promise with no idea if the best candidate (who would agree to the appointment) would be a woman.
Psaki is a lying, 2-bit pony soldier if she wants to sell that narrative. She even included that Trump announced he would select a woman "just over a year ago." Check a calendar. The official announcement was Sept 26, 2020. The video going viral today of Trump picking a woman was from Sep 20, 2020. This was not even close to the same ballpark as what Biden promised. Trump was "leaking" is actual pick was, in fact, a woman. I don't think anyone can call that a "promise."
"I bought you a new gun, son. It'll be under the tree Christmas morning in just 4 days. All I can tell you is it's a top of the line 1911."
That's totally different than, "I promise I'll buy you a top of the line 1911 for your birthday or Christmas next year." At that point, he hadn't decided on which gun to buy.