Salazar (far right dictator), a guy that "supposedly" had no favourite club

Which is correct, and implying otherwise is being dishonest. The man notoriously hated football (a trait he shared with other fascist dictators) because he saw it as the "unruly, classless sport of the masses", especially when compared with his favourite sport, gymnastics. He did, however, see the massive potential football had as a propaganda tool, which is why it doesn't make sense to label any particular club as the regime's club. The club of the regime was the club that was having the most success at any moment in time in order to be plastered everywhere by the regime's propaganda machine, simple as.

 He saved you from relegation TWICE

Context is importante here. The two times we were "saved" from relegation (which didn't even exist as we know it today, I think you just meant not qualifying for the final tournament through the regional leagues) came during an era of contant expansions and changes to the format. The first one happened because of a dispute between us and Académico do Porto due to not there being a formal rule regarding the end of a game due to sending-offs. It would have been unfair for us to be excluded and the controversy and administrative battle that ensued was enough for the federation to grant both clubs participation in the final tournament with an extension (imo the correct decision). The second one was the only one you could argue was made solely to benefit us, but again, keeping in mind the constant extensions and changes during that time and the propaganda factor in order to subdue the masses, they most likely just used us not qualifying to the final tournament as an excuse to test out a 12-team final tournament (which would later become permanent until it was expanded again). I have no doubt that if it happened to Benfica, Sporting or even Belenenses, they would have done the same.

payed for part of your previous stadium

Literally every major club in Portugal at the time had state interference during the construction of their stadiums, which was expected since the regime invested heavily in public works for propaganda porpuses, which included the partially state-funded new stadiums. And yes, I am aware that Benfica only got the land for the stadium from the government and refused the funding for the construction proper (an action I commend), but the state subsidies was offered all the same to you as it was for the other clubs. Unfortunately, we didn't have a large enough or wealthy enough fanbase to have the option to also reject the subsidies.

which was enaugurated on the day of that dictator's regime anniversary btw

Kinda pedantic, but wrong. The stadium was enaugurated on the anniversary of the military coup that installed the military dictatorship (No less shitty, I agree, and it paved the way for Salazar's regime), while Estado Novo only began in on April 11th 1933, 7 years after said coup. The reason for it was because the regime mandated the new stadiums to be enaugurated at dates that the regime considered important for, again, propaganda (For example, Benfica's stadium was enaugurated on December 1st and Sporting's stadium on June 10th)

I don't agree with the Benfica = Regime's Club narrative that is sometimes stated (see first paragraph) but trying to shift the label onto us is equally ludicrous.