This is indeed useful additional information. Thank you.
You have confirmed that at least one of the two suggested workarounds is consistent in its efficacy. In using a VPN connection, you are “tunnelling” your traffic past the source of the issue.
Diagnostic testing suggests that the issue of some types of Mail message loading very slowly, with a consistent and repeatable delay, is linked to Apple’s Private Relay service. I’ll try to keep this description relatively simple and non-technical…
Apple introduced its Private Relay (Beta) service in iPadOS15. Its purpose is to provide additional privacy and security for unencrypted network protocols included within your internet traffic (e.g., DNS and basic http protocols); these “in clear” protocols leak significant information - and can be intercepted and manipulated by almost anyone along the path from source to destination. Private Relay encrypts and anonymises this otherwise unprotected network traffic using a client element and a double-hop relay via infrastructure servers.
The Private Relay client element “shims” the device network stack. Whether Private Relay is locally enabled on the device or not, the network shim is ever-present - and as such has the capacity to influence processing of network traffic on your device.
With the VPN client enabled, your internet traffic completely bypasses both the client and server elements of Private Relay. While VPN is enabled, your Mail is seemingly retrieved and processed without issue.
Testing also suggests that the problematic processing of network traffic is similarly ameliorated when Private Relay is itself enabled - this feature perhaps being enabled by the majority of iCloud+ subscribers. When processing traffic via Private Relay, a VPN tunnel workaround is not required to resolve Mail performance issues. Interestingly, the issue with Mail does not appear to occur when using a Cellular hotspot connection.
More analysis and testing is required - hopefully obtaining additional information from similarly affected Users concerning their network configuration and device settings. If the cause of the issue is confirmed, use of available workarounds will continue to be required until such time as Apple resolves the underlying problem.
In the meantime, subscribing to either (a) the base iCloud+ tier, or (b) a full service VPN provider will restore nominal Mail performance pending correction by Apple. Given the relative low-cost of iCloud+, coupled with the ability to cancel at any time, this may be the most appropriate of the available options at this point in time.
I hope this information and insight proves to be useful to you.