Let me parse the inconsistencies for you.
Prior to the Rostelecom cup, when Scherbakova withdrew, the Tutberidze camp claimed that it was pneumonia and nothing more. They forcefully denied any possibility of Covid-19. Why? Because even the slightest suspicion would have implied that the entire Khrustalny site must be quarantined, thereby also precluding the participation of several of their other skaters in the Rostelecom cup, including Valieva and Zagitova. So their official statement at the time was that they were absolute certain it could NOT have been Covid. Because if they could not rule out that possibility with 100% certainty (or worse, if they knew she had been diagnosed with Covid), they are implicitly responsible for the spread of Covid at Rostelecom.
Fast forward to Russian Nationals. To provide extenuating circumstances for Scherbakova's mistakes in the SP, aggrandize her win, and push the 'heroism' narrative, camp Tutberidze made public statements along the lines that she skated with 38 C fever, still not fully recovered from pneumonia, and refused to let her fever checked. Naturally, this prompted the legitimate question of why Shcherbakova broke the rules, as high fever is a typical Covid symptom, which is why skaters with high fevers are not allowed to compete as a precaution measure. Given that they previously had stated that she did not have Covid, her high fever implied that she could potentially be infected at that moment, and by entering the clean zone there was a risk she may have spread the infection to other skaters and/or coaches. When they realized the blunder, Gorshkov tried to do some damage control by making a public statement reproduced in the article that was linked by other posters above. In that statement, it was claimed that Shcherbakova in fact had had Covid "a long time ago", and hence that by competing with a fever at Nationals she did not in fact endanger the health of other athletes, as they were certain she had had the disease before and was no longer a potential threat to other participants.
Therefore the following scenarios are possible:
(1) They lied pre-Rostelecom and were in fact certain that she had Covid, in which case they bear a huge responsibility for sending skaters that had been in contact with her to Rostelecom and infecting several athletes like Liza T, Aliev etc.
(2) They lied in the post-Nationals statements when they claimed she had already had Covid a long time ago, and in fact they allowed Shcherbakova to skate despite showing a major Covid symptom, in which case they put Russian Nationals participants at risk.
(3) They were never certain whether or not she had Covid at any given time point, so they lied both pre-Rosetelecom and at Nationals, in which case they endangered the health of other athletes at both events.
What is certainly NOT possible is that they could have told the truth on all occasions, as this would imply that they were 100% certain that Scherbakova both had and did not have the disease in November -- which is a logical impossibility. Ergo they must have lied on at least one occasion.
Q.E.D.
Those aren't inconsistencies.
1. Absolutely no one has said that she had a positive COVID test ever. Even the first article everyone is quoting never says she did have one. The only things that where confirmed which is that she had pneumonia. Even the article everyone is quoting agrees with that statement. No one has said definitely that she DOES/DID have a positive COVID test (which by the way is the only way you can diagnose COVID.)
2. The diagnosis of pneumonia is the only one she has ever officially been given by anyone. Even the one article saying she had coronavirus says she had pneumonia. Those are also not mutually exclusive.
3. Fast forwarding to Russian nationals. Here Anna by ALL accounts tested negative for COVID. She did have a fever but it's not against the rules (for Russia) to skate with a fever. Sofia S was allowed to skate her SP at test skates WITH a fever (which she later said was a cold.) So this part is false: "skaters with high fevers are not allowed to compete as a precaution measure." It actually isn't a rule. Also a fever is ALSO a pneumonia symptom.
4. Therefore, by all account, she DOESN'T break the rules by skating with a fever as (1). She tested negative for COVID and (2). Skating with a fever is allowed (in Russia).
5. The only things you can say 100% is in regards to a COVID test and those are only 30-40% accurate. And Anna tested NEGATIVE. That could have been a false negative but it was a negative none the less.
So therefore, looking at your scenarios:
(1) They lied pre-Rostelecom and were in fact certain that she had Covid, in which case they bear a huge responsibility for sending skaters that had been in contact with her to Rostelecom and infecting several athletes like Liza T, Aliev etc.
Response: They didn't lie. They said she had pneumonia and withdrew her for that reason. That she had pneumonia has been confirmed by all sources (Anna, her parents, her coaches, the Fed) and they all agree. Pneumonia was the only thing she was actually diagnosed with. And all sources agree that she had it.
(2) They lied in the post-Nationals statements when they claimed she had already had Covid a long time ago, and in fact they allowed Shcherbakova to skate despite showing a major Covid symptom, in which case they put Russian Nationals participants at risk.
Response: They didn't lie. They (Anna or her camp) never claimed she had COVID. She was allowed to skate with a fever because she's allowed to skate with a fever under Fed regulations, as they stand. (Same with Sofia at test skates.) Regardless, here Anna tested negative for COVID. The only regulation is a negative COVID test which Anna had.
(3) They were never certain whether or not she had Covid at any given time point, so they lied both pre-Rosetelecom and at Nationals, in which case they endangered the health of other athletes at both events.
Response: They do seem like they weren't certain if she did have COVID or not. Regardless, at Nationals (at least) she tested negative, despite having a fever. Her mother herself seems to think she might have had COVID but each time she was tested her test was negative. So, by all rules, she was allowed to compete.
She's also not the only skater to skate at events when not completely healthy; however, considering she tested negative, she didn't break any rules.