They did NOT abdicated the power. They, meaning their republican members, are actively using power to achieve or defend republican ideological goals. Democrats are not fighting as they should, they tend to be centrists seeking to accomodate.
But, there was no abdication. There is an intentional cooperation.
It might be cooperation through abdication, but it's still abdication. They are choosing to allow the executive to do things that would be under their control.
I'd say choosing to let the executive execute reckless tarriff policies counts as "abdicating power". If they really believed in their power, Trump would just need to throw tarriff policies at congress and they can approve it with their majority house and senate votes.
Likewise, the Supreme Court putting an immunity clause right before Biden left feels like abdication. Again, if what Trump was doing was just, it'd be easy to interpret it in his favor, 6-3. But instead they gave blanket immunity. It can be intentional cooperation and still be abdicating.
But, there was no abdication. There is an intentional cooperation.