macOS Big Sur Dictionary.app doesn't use system proxy
This phenomenon is not unique to Big Sur—it likely dates back to when the Dictionary application was first introduced in Tiger. @1110101001 did some reverse engineering to figure out what's going on.
DictionaryServices.framework makes network connections via the now-deprecated CFHTTPStream. According to an Apple engineer and Apple's own code, any software which uses CFHTTPStream will ignore the system's proxy settings, unless the developer goes out of their way to add a few extra lines of code.
To fix this problem, we'll need to inject some code which does what the original developers did not—tell the app to apply the system's proxy settings before running CFHTTPStream.
First, compile the following code (e.g. clang -framework AppKit -framework Foundation -o ProxyFix.dylib -dynamiclib /path/to/code.m) to create a library we can inject. This was also mostly written by 1110101001; I tweaked it to work with apps that use two-level namespaces.
#include &lt;stdio.h&gt;
#include &lt;objc/runtime.h&gt;
#include &lt;Foundation/Foundation.h&gt;
#include &lt;dlfcn.h&gt;
#include &lt;AppKit/AppKit.h&gt;

#define DYLD_INTERPOSE(_replacement,_replacee) \
    __attribute__((used)) static struct{ const void* replacement; const void* replacee; } _interpose_##_replacee \
                __attribute__ ((section (&quot;__DATA,__interpose&quot;))) = { (const void*)(unsigned long)&amp;_replacement, (const void*)(unsigned long)&amp;_replacee };

CFReadStreamRef myCFReadStreamCreateForHTTPRequest(CFAllocatorRef alloc, CFHTTPMessageRef request) {
    printf(&quot;Injected ProxyFix!\n&quot;);
    CFReadStreamRef ref = CFReadStreamCreateForHTTPRequest(alloc, request);
    CFDictionaryRef systemProxyDict = CFNetworkCopySystemProxySettings();
    CFReadStreamSetProperty(ref, kCFStreamPropertyHTTPProxy, systemProxyDict);
    return ref;
}

DYLD_INTERPOSE(myCFReadStreamCreateForHTTPRequest, CFReadStreamCreateForHTTPRequest);

We now need to insert this library into the Dictionary application. Luckily, macOS comes with a built-in mechanism for injecting code in the form of DYLD_INSERT_LIBRARIES. If you, like me, are running an ancient and lovably-hackable version of macOS such as 10.9, all you need to do is run your app after setting this environmental variable. For example, run in Terminal:
DYLD_INSERT_LIBRARIES=/path/to/ProxyFix.dylib /Applications/Dictionary.app/Contents/MacOS/Dictionary

If you're running macOS 10.6 or below, or if the application isn't code signed (possibly because you removed the code signature via optool or similar), you can also add this environment variable to the app's Info.plist, so that the library is injected automatically.
defaults write /Applications/Dictionary.app/Contents/Info LSEnvironment -dict DYLD_INSERT_LIBRARIES @executable_path/../Frameworks/ProxyFix.dylib

Unfortunately, newer versions of macOS have additional security features to prevent code injection. Starting with 10.11, you will need to disable System Integrity Protection in order to use DYLD_INSERT_LIBRARIES. On the newest OS's such as Big Sur, you may (or may not) need to take further steps as well, such as disabling AMFI—I'm not entirely familiar with all of the new security checks Apple has layered on in recent years.

P.S. If you're running 10.6 – 10.9, I wrapped this up into a little installer which helps you set up a proxy, and then applies the above patch to the Dictionary app. Without the aid of a proxy, the Dictionary app's Wikipedia functionality no longer works at all on these systems. https://jonathanalland.com/downloads/wowfunhappy-https-proxy.dmg