Apple Mail Preferences Pane just "hangs" after Big Sur Upgrade

Perhaps the EtreCheck can put some light on the underlining issue(s) ! A quick System Report and see what the OS says regarding the Battery Health and # of full battery Cycles. While at it - try SMC Reset 3 times in a row

You wrote " Also, since the Big Sur Upgrade battery life is reduced to almost 25% and the fan is on constantly " the reduced battery and fan issue are an indication of high CPU and or Memory usage. That is indicative of some Runaway process and / or Third Party Software / Extension that is playing up and may be part of the Mail Preference beach-balling. Suggest opening the Activity Monitor >> View >> View ALL Processes and checking CPU Usage and or Memory Usage.

During the Clean Install Did you use Migration Assist ? Sometimes, the migration re-introduces a pre-existing unresolved issue back into the Clean Installation. Thereby negation of the clean installation.

Should that not be the case - there is a very good and reputable Application called Etrecheck writer by a very respected Community Member that can be used to view and collect hardware and software information. It can produce a Report for personal viewing or posting to the Forum. It does not collect any personal information and is free to use. It would be a good idea , if going this route, to Give it Full Disk Access via Security& Privacy >> Disk Access and Enable Full Access.