Trump was up against the same legislation that Biden is. But that didn't stop Trump, you knew he was trying. No so much with Joe.

Some of that is perception, not reality. Because Trump and Biden face very different political incentives.

For example, one of the things that Trump tried to do was to adopt by administrative rule a "First Safe Country" requirement - basically the one that many folks think is already part of international law (but isn't) that a migrant has to apply for asylum in the first country they get to where it's safe for them. Of course, that was shot down by the courts.

When immigration levels started to rise after Covid receded, Biden also tried to implement that same policy. They tweaked it to try to get it past the courts, but it was essentially the same. But again, the courts have held it's illegal (again, for many of the reasons we've discussed at length on this thread):

nbcnews.com - Judge rules biden immigration policy calling invalid

But the difference is that Trump has a very different political position than Biden. On immigration, Trump gains if he can fail loudly; Biden gains if he can succeed quietly. Trump has every incentive to make sure that everyone knows he's trying, as you point out. His base wants to reduce the number of asylees, for reasons apart from reducing the collateral impacts of the "waiting around for hearing" population. He gains politically if he has a very restrictive administrative rule that fails. So his team made sure everyone knew about it - that everyone "knew he was trying." And if you get even some of your news from conservative-leaning media, they would have run that story heavily.

Biden has the opposite incentives. He wants the problems of the "waiting around for hearing" population to actually get solved, but he doesn't really want his base to know that he was doing anything to make immigration policy stricter. He just needs to fix the problem (so it disappears from the headlines), not have anyone think he's an immigration hardliner. So when he does the exact same thing as Trump, and the exact same thing happens, Biden doesn't have any incentives at all to have anyone know about it. So his team isn't out there trumpeting the proposed rule and letting everyone know that Biden tried and failed. And conservative-leaning media isn't going to let their audience know about that, either.