This definitely feels incredibly significant. The Soviet Union tried and failed 4 or 5 times to launch a rocket with this many engines, but now we're able to nail it on the first try aaaand land the boosters.
I am pretty sure that SpaceX was able to achieve what they did today also because they studied the Soviet N1 rocket and learned from what the engineers at that time had to figure out from scratch.
The other thing is that the N1 Moon rocket was a very different design - a single booster with many small engines, so incredibly difficult system to control, especially given the state of technology 50 years ago. Falcon Heavy is more similar to the successful Energia booster - core + strap on boosters - that was originally designed for the Russian shuttle. Or the Angara series.
In comparison, the Saturn V used only 5, they were just that much bigger. It's widely regarded that the 5 vs 30 was the difference as to why Saturn V was successful and N1 was not, as the Soviets simply had to roll too many dice in a situation where a failure resulted in complete mission loss.
It's a lesson in system engineering, particularly around failure durability and parallel vs serial critical subsystems.
In this sense R-7 is remarkable because it has a good overall success record (most launched rocket) and 32 chambers working at liftoff. Some of those chambers are rather small - about 3 metric tons of thrust, about as much as main chambers on British launcher Black Arrow - but still.
You're right, though, the R-7 is a fantastic achievement not only for the chambers, but also considering how many engines and pumps it has. All those spinning, moving parts are another point of failure and they're all necessary for success.
If Soviets wanted something modern, they had to reinvent it from scratch - or steal it. They were fairly good at both. Whether it was a computer, transistors or entire designs. The results were usually very simple designs where little could go wrong and that didn't need complicated technology - which wasn't available. E.g. the Soyuz capsule vs. both the Apollo and Space Shuttle craft.
I lived in a former Soviet bloc country and I can tell you that getting even silly components like LEDs required superhuman efforts. The few that were made domestically ended up in industrial uses (or exported to USSR) and importing anything from abroad was almost impossible. We had a black & white TV full of tubes until late 80s at home - color solid state TVs didn't become available until 1988 or so (and sucked big time).
That being said, SpaceX is taking a much more pragmatic and efficient approach to building rockets with far less bureaucracy. This is the epitome of private sector efficieny over government projects.
The problem is lack of meaningful competition, rather than government vs. industry; governments can be very good when competing with other governments.