Leaving aside the obvious claim that Tamamo’s 9-tailed form in her memories may not be a perfect match for her form in reality, Tamamo’s legend didn’t just come out of nowhere. Foxes of all varieties were common figures in Japanese folklore, both just real foxes and gods who chose to take the form of foxes, and legend had it that foxes would grow an extra tail for every 1000 years they lived, and any regular fox that grew 9 tails would ascend to godhood. With that understanding in place, a fox that was already a god growing 9 tails being extremely powerful is not a logical reach at all.
Not to mention there is absolutely no reason, in the Fate universe or otherwise, to assume that all Divine Spirits are equal in power. Pantheons are normally stratified by power level, and in many cultures, sun deities were at the absolute top of the pile. There’s not really enough Divine Spirits running around the in the Fate world for us to go creating any substantive theories on how they’d function in all scenarios, nor enough Beasts for that matter, and most of the ones that do exist exist in FGO, where the rules are explicitly stated to be quite different due to the nature of Chaldea’s Servant summoning system as opposed to a regular Holy Grail War operating using the 3rd Magic or the Mooncell’s digital summoning process, which are both substantially different in nature. But it is worth noting that all the goddesses in Babylonia can exert their full Authority over Tiamat - namely Ereshkigal, seeing as her Authority does actually come into play - so I see no reason why Amaterasu, one of the most powerful deities in Shinto belief, should have trouble standing up to a Beast when a cabal of fairly minor Mesapotamian goddesses managed against Tiamat just fine.
It’s not “inconsistent” for every piece of lore not to play out on screen in the most obvious possible way, and especially in the context of CCC, if your suspension of disbelief can handle an absurdly powerful supercomputer of debatable origin housed on the Moon, capable of summoning the spirits of dead heroes from the past, present, future and even from different pasts that never occurred in the world of CCC, a glitched-out nurse AI breaking herself into 6 pieces and fusing the other 5 with various goddess data to create autonomous sentinels and a nun so goddamn horny she literally moves between different continuities to attempt to put the entire Earth inside her vagina, I really fail to see why 9-tailed Tamamo, who we never see in action, having a totally off-the-charts power level that is consistent with the things she was able to do in lore, is what is really breaking your immersion here. Fate isn’t science fiction, at best it’s science fantasy, which is a legitimate genre with its own tropes and rules and standards. If it pisses you off that much, I may politely suggest that you stop reading it and restrict yourself to more conventional hard science fiction that’s tailored to your tastes.