There is a difference between politics as usual and what you propose. Politics as usual allows for mutually exclusive goals because it acknowledged nobody can win everything. Compromise is built in, even in backroom deals. What you propose isn't the same, because the mutually exclusive goals cannot be compromised on. It's not two sides or 'two sides' going at it in competitive terms, it's them supposedly working alongside each other. In such a scenario, goals must be achieved, compromise after the fact is imposible.
Assuming they aren't after the same base goals, just with a different lick of paint. If the destination is the same, the path you walk is just a distraction. or something more philosophical.
Now, as to your proposals. Gay Marriage was on a long track to be at least 50/50 support when it was found to be constitutional. While 15 years ago gays adopting was a hot topic, even back then gay marriage itself was on the upswing for support. Also, it wasn't a gay marriage bill, it was SCOTUS finding that restrictions against gay marriage were unconstiutional. All in all, this example is not analogous to anything pushed forward by this admin.
What's the support for the vax mandate? NOT how Biden is going about doing it, but for the actual mandating of jabs and passports becoming a requirement for travel/work/entertainment? The waters are muddied because we can't see how popular/unpopular the idea of passports is, only Bidens idea of using 'force'. The old saying' "can't see wood for the trees" is the best way i can describe it.
As for gay marraige, it wasn't popular. It won through apathy. Not enough people cared, or had reason enough to stop it, rather than it having 50% support and 50% against. Ironically, those against gay marraige said it would lead to degeneracy in society. They were right.
You provide a brief list after, so to knock them down quick: Trans Rights can be and is controversial, to the point that we have the last sitting president moving against Trans people in the military to very, very little condemnation from the center. As in, it was a net -support-. Airport security is here to stay because we have had twenty years to accept it. No real groundswell ever rose to opposite it nor was there significant disapproval at the time. Again, not analogous to here. Finally, Spying. Technically gutted under Trump when he didn't renew the big bill for it, see the prior one for again a large part of why it is here to stay.
Again though, how many people support trans rights, vs don't care enough either way/don't want to be seen as a bigot. You couldn't oppose extra airport security after 9/11 because it was a bit daft to do so, given the circumstances. 10 years later though? We don't need it, but nobody cares enough either way to do anything about it. Wouldn't it be political suicide to say "we're going to remove that thing that people feel makes them safer"?
Meanwhile, I can provide you convenient counters. Trump and Biden both spent a -lot- of time stripping out what their predecessor did.
Trump removed what Obama did, Biden, Obama's VP removed what Trump did and re-instated what Obama did, just reversing the reversal of Obamas policy. Uno.
Now, as for Biden being able to 'throw the might of congress". No. Simply no. The problem is that this is largely a states right issue, HORRIFICALLY unpopular among the general populace, and would see immediate resistance to it. Unlike your prior examples, it wouldn't get to be here and stay here because its always been here and wasn't opposed when it was put it.
He doesn't have to do it, he just has to say it. The general populace gets their information from headlines, not details and information. And on that, the general populace are jabbed. 54% have been poked, so why would they, as a majority, kick up a fuss about something that will have no impact on them?
Sure, you may get a few arseholes shouting about on twitter for updoots, about how they disagree with restrictions etc, but they still got the jab. Do you think they care if people can't go travelling? Will they care enough to stand up for the people who haven't been jabbed?
Both the jabbed and un-jabbed can think Biden is a useless twatt, but only the unjabbed will kick up a fuss to stop restrictions happening. Just like those people in the 90's who said "don't let gays get married, it will degenerate society". And where are we today? We are at a place where misgendering a fat old bloke in a wig, sees you marched out of your job.