Greetings, and welcome to this Apple (user-to-user) Community!
Re: "Mail cannot open mailbox due to 'Partition pending requests queue is full' error"
Am no expert in this area, and, as Apple users, just like you, we have no access to your accounts or details etc. to check this out for you. (Apple is unlikely to participate.)
Also: We can not guess which hardware model (Mac, iPhone, iPad ?) you are using, or which OS version (eg: MacOS26, iOS 18,) is installed, in order to help troubleshoot.
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Re: "The server returned the error: Partition pending requests queue is full: part_max_pending=128 pool_key='ckrpc - http2://p177-xr.ckdatabaserpc.icloud.com:81 {prtn=177}'
Seems there is not enough memory / storage available for Mail to operate smoothly. We'd likely only be guessing if we assumed where that capacity needs attention, without more details. I could be wrong, yet this reply provides opportunity for others with more expertise in this area to respond.
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If needed: Apple provides a Mail Support website (info. / support / contact options etc.)
Mail - Official Apple Support