I'm also having horribly slow performance in Mail recently. I'm running Big Sur (11.3). I've tried with my local WiFi and using my iPhone (with LTE) as a hotspot; there is no apparent performance difference. Browsing web pages and streaming videos is working fine, so it doesn't appear to be a general network performance problem.
If I open the Activity window in Mail, it shows progress bars for "Moving Messages", "Checking for mail...", "Downloading Messages". The Moving Messages progresses very slowly; it took 1 minute 17 seconds to go from "8 of 98" to "9 of 98". Downloading Messages hasn't changed in the last several minutes (347 of 509). Looking in Activity Monitor in the Network tab, it shows pulses of activity about every 20 seconds, with almost nothing in between. The Sent Packets and Rcvd Packets columns for Mail change by maybe 1 or 2 packets every 10+ seconds.
Mail's % CPU is mostly 0.0, with brief jumps to 0.1 every few seconds. The various Mail Web Content, Mail Networking, MailCacheDelete processes are all consistently at 0.0% The system is consistently around 95% idle. So it doesn't look like anything is CPU bound.
I tried moving aside the ~/Library/Mail/V8/MailData/Envelope Index* files (while Mail was not running), and that did not make any difference.
I'd be glad to gather logs or samples, if you (Apple) will tell me how to gather the data you want, and where to send it.