Point out the litigation section. It is questionable legally, which is why it was stayed several times. There were appeals pending in the courts when Biden took office (next section after "litigation". From what albaby has explained, it was not likely to survive all the challenges. Once they are here, you can't mini-deport them unless Mexico (for example) agrees to it. They have the legal right to apply for asylum, and if they pass their initial interview, remain until they have their court date.

Trump also had two years of Rep control of Congress, and also did nothing. He tried to EO his way through, but the courts kept shooting his EOs down.

No, it would be a lie to say it is all the Rep's fault. This issue has been festering for decades. Back in the 80s and 90s, it was how many people think it still is: Mexicans (mostly) sneaking across the border to find work. But that hasn't been true for maybe 20 years now. They are asylum seekers. Whole different set of rules, completely different circumstance. And it's not just Mexicans. It's a lot of Central and South America, plus China, and Ukraine, and Russia...just to name a few. Fleeing war, civil violence (gangs, warlords, whatever), government-sponsored violence (repression and persecution), etc. And we are legally obligated to process every one of them that crosses our border.

The Senate bill would have tightened restrictions, possibly even to the point that part of it might have been struck down. We'll never know because -this time- it is squarely on Trump and Johnson. I can't say "Reps" here because Reps were in the room at the negotiating table, and were hammering out a compromise that under almost any other circumstance, a large number of Dems would not have agreed to. I'm sure the progressive wing is secretly thanking Trump and Johnson, because they especially didn't want that bill.