This kind of gap between peak period and non-peak period is pretty standard though, no? I feel like it would need to really stand out to conclude that the wicket keeping was holding back his batting by a lot.
IIRC a lot of players had ridiculously hot streaks around the time of Sanga's peak. Ponting obviously has his god-tier years, but guys like Younis, Yousuf and Chanderpaul also had long streaks of obscene run-scoring. I'm not sure if there was a time when there was daylight between him and his contemporaries, which was clearly the case for Tendulkar and Lara in the 90s.
I mean I still feel like he's way underrated, but this is pushing it too far imo.
27 runs on average is an improvement of 67.5% from 40. I would not describe the gap as standard tbh. I would be extremely surprised if a single cricketer (with a decent sample size of tests both as specialist batsman and designated keeper) had anywhere close to an improvement as a batsman when they were not the designated keeper. Someone who is often cited in this regard, Alec Stewart had a batting average of 34.9 as keeper and 46.7 as designated batsman. That difference is huge but not quite comparable to Sanga even if we account for the absolute run difference being lower due to the start off point being lower.
He basically went from what would be a barely test standard batsman for his batting friendly era to someone who averaged about 10 runs more than what you'd expect from an all-time great batsman for his time. To illustrate the point a different way, he had 10 double hundreds in 64% of his career while not keeping and 1 double hundred in the 36% of his career keeping. He became someone who consistently made 150+ scores as pure batsman which traditionally are extremely rare as the designated keeper, and would be much harder in Sanga's case because he was keeping along with batting No.3 a majority of the time.
You have a point about other batsmen also having red hot streaks during Sanga's career but IMO he was the best of the batsmen whose effective careers were (almost) exclusively in the 2000-2015 period. He was the one to do it most consistently and brutally in a variety of conditions over 15 years. This was even more true when he did not have to keep anymore and averaged over 65 for the year 9 year period from 2006-2014. He has the record for the most amount of double hundreds apart from Bradman and I think 8/11 double hundreds forced a result and 1 against Pakistan saved a match from what looked like a clear draw. He was excellent in spinning, bouncy and swinging conditions.
The only one to keep up with him over the entire 15 year period was Kallis but he was less likely to relentlessly shut down the game with a big century when he got going IMO, even in favourable batting conditions. I'd say Dravid and Ponting have significant cases against them over Sanga in terms of not being as good for quite as long and also failing a few major challenges each, like Ponting in India again and again or Dravid against quality seam bowling in places like SA/Australia. I'd say Kallis/Dravid/Ponting are quite close to Sanga overall though. Waugh is not far behind either.
Who, apart from Tendulkar and Lara, do you think was better than Sangakkara in the 1990-2015 period?