I've seen a lot of this sentiment recently, and I just don't think it's that true in a longer term. Historically, there a ton of examples of both parties extending executive power, trashing norms when it suits them, etc. Obama and Biden did a ton of executive orders to push things that they couldn't achieve legislatively. I mean, the office that is now Doge was created by Obama outside the normal channels of congressional approval. Some of their actions got knocked down by the courts. Some of Trump's will as well.
However, a couple reasons it definitely seems like the Republicans are ahead of the game on this now...
1. Democrats have been way more effective enacting their agenda through the bureaucracy and regulations, and achieving things via regulation and department edicts that they can't achieve by lawmaking. Someone else mentioned Chevron, and that's pretty relevant here, because that's the way Democrats have traditionally end run around the proper procedures. And that happens much more quietly.
2. Until recently, Democrats were way, way more effective than Republicans at legislating through the courts. Often in conjunction with #1. Republicans have gotten good at this too now.
So the two ways that Democrats had a massive advantage on non-legislative action have been neutralized a bit or Republicans have evened up.
3. Mitch McConnell was probably the best at his job since Lyndon Johnson. He is one of the absolute all-timers, and ran circles around his Democratic counterparts. You don't have to like him, but there's just no comparison between him and Schumer. That's just the coincidence of raw political talent, and is not indicative of Republican Senate leaders that preceded him or are likely to follow.
4. Trump doesn't really GAF. That isn't traditionally true of Republicans, even Trump's first term. Some of what he's doing is legitimate within his power, some of it is dubious, and some of it is ridiculous. We won't know for a bit what he's actually accomplished.