Another such project was Buran/Energia, which while not a carbon copy of Space Shuttle was an outcome of matching "what the Americans have".
Buran doesn't use integrated reusable engines with the external tank, so there's no awkward mix of solid boosters. Plus, Buran has a fully functional emergency ejection seats for all crew members. More so, the Buran had automated flight from the outset and meant that Buran could be lauched without anyone and be landed fully automatic.
Energia could be launched by itself, and carry about 100 tons which is about 3 times the shuttle's capacity, and being a seperate system makes so much more sense than the booster + fuel tank mix of the Space Shuttle system.
In general, Buran, from an engineering point of view, was a fantastic piece of work and although might have been inspired by the Shuttle initially, it definitely improved on the Shuttle design.
It's truly sad that the Buran was discontinued only after one flight. It deserved more time in the sun to shine.
But yes, the USSR almost outdid the USA on star wars, if it weren't for some software error.
https://www.youtube.com/watch?v=s4XgCRnqwpg
https://nationalinterest.org/feature/the-rise-fall-the-sovie...
More details on the project in this article (in Russian) https://warspot.ru/19630-tayny-polyusa
Buran had other interesting features, like non-toxic propellants and longer ability to stay on orbit. It's not that Soviets always learned from their mistakes and made better systems - sometimes they couldn't, and sometimes the problems were internal to the system, like grounding of TKS after Chelomey's death - it's that sometimes this approach did lead to improved results. Soviet engineers were quite capable in aerospace.
Regarding economics of Tu-144 flights. I've heard that economics of civil aviation in USSR was rather weird - political pressure dictated having civil aviation, economical realities dictated subsidizing most - not only Tu-144 - flights to keep them affordable, yet this approach also had side benefits in keeping industry, which essentially was tailored for military orders, occupied with projects, testing, maintenance, learning, education of specialists, even international sales.
I am not quite convinced about the test limitations for the Polyus station; I mean according to Anton Chechov, that (laser) gun in the picture would have to shoot, at some point. Maybe that would have resulted in much earlier conflict between the political leadership and the military industrial complex, who knows. They mentioned that that they had the Buran launcher fuelled up and ready for launch, while attempts were ongoing to push the decission for the test launch through, I mean that sounds like of lots of politics was going on behind the scene, assuming that this exercise would have a significant risk and cost a non trivial amount of money.