I had problems with the last firmware update, too.
With prior version of AC, attempting to access the Animate-II page gave an error saying a "core service" needed to be updated. Clicking "Update" would close AC, bring up an update dialog, declare success, then restart AC. Further attempts to access the Animate-II page resulted in the same "loop", over and over. Trying to install the update from the "Update Center" screen gave the same result.
After upgrading AC to 5.4.10.0, I still had the same issue. I uninstalled AC using the uninstall tool, and reinstalled it. I was then able to perform the update. However, AC kept telling me an update was needed. Sometimes I could access the Animate II page, but most times it would tell me an update was required, over and over.
What I *think* fixed it was this: Once I was able to get to the Animate II page, I went to the "Firmware Update" tab there and clicked "Check Update". This just took me to the Update Center again, where I clicked "Check for Updates" again -- and it found none, because everything was up-to-date. But since then, I can consistently access the Animate-II page without any problem. I don't know if this different "route" to the Update Center fixed something, or if AC just finally overwrote whatever was causing the problem. But you might give that a try, assuming you can get to the Animate-II page and it's "Firmware Update" tab.
For reference, here are the component versions installed for mine:
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Z690-E, i9-12900k, 2x16 DDR5, 980pro nvme x3, Ryujin-II 360, Strix Animate-II, Evga 3090 ftw3