Is this Mac owned by your employer and therefore managed by your IT department? Do you see a Profiles icon in System Preferences? You would only see that if it's a managed device. If so, I wouldn't attempt to upgrade it without your IT departments assistance. Things could break badly as the device might fail to boot, etc. Depends on what the employer has installed on the Mac.
One thing you could try if it is not managed by your IT department would be to attempt installing 11.4 via external USB bootable drive. Providing you have "Install macOS Big Sur" in /Applications and it is in fact 11.4. You can create a bootable USB installer using Terminal.
First make sure you have 11.4 downloaded in /Applications/Install macOS Big Sur and in Terminal issue the following command:
cat /Applications/Install\ macOS\ Big\ Sur.app/Contents/Info.plist
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<dict>
<key>Application-Group</key>
<string>AirPort</string>
<key>BuildMachineOSBuild</key>
<string>20A241115</string>
<key>CFBundleDevelopmentRegion</key>
<string>English</string>
<key>CFBundleDisplayName</key>
<string>Install macOS Big Sur</string>
<key>CFBundleExecutable</key>
<string>InstallAssistant_springboard</string>
<key>CFBundleGetInfoString</key>
<string>Install macOS Big Sur, Copyright © 2007-2021 Apple Inc. All rights reserved.</string>
<key>CFBundleIconFile</key>
<string>InstallAssistant</string>
<key>CFBundleIdentifier</key>
<string>com.apple.InstallAssistant.macOSBigSur</string>
<key>CFBundleInfoDictionaryVersion</key>
<string>6.0</string>
<key>CFBundleName</key>
<string>Install mac OS</string>
<key>CFBundlePackageType</key>
<string>APPL</string>
<key>CFBundleShortVersionString</key>
<string>16.6.01</string>
<key>CFBundleSignature</key>
<string>????</string>
<key>CFBundleSupportedPlatforms</key>
<array>
<string>MacOSX</string>
</array>
<key>CFBundleURLTypes</key>
<array>
<dict>
<key>CFBundleURLName</key>
<string>Open Install OS X URL</string>
<key>CFBundleURLSchemes</key>
<array>
<string>x-install-osx-assistant</string>
</array>
</dict>
</array>
<key>CFBundleVersion</key>
<string>16601</string>
<key>DTCompiler</key>
<string>com.apple.compilers.llvm.clang.1_0</string>
<key>DTPlatformBuild</key>
<string>12E6178j</string>
<key>DTPlatformName</key>
<string>macosx</string>
<key>DTPlatformVersion</key>
<string>11.4</string>
<key>DTSDKBuild</key>
<string>20F70a</string>
<key>DTSDKName</key>
<string>macosx11.4internal</string>
<key>DTXcode</key>
<string>1240</string>
<key>DTXcodeBuild</key>
<string>12E6178j</string>
<key>LSApplicationCategoryType</key>
<string>public.app-category.utilities</string>
<key>LSHasLocalizedDisplayName</key>
<true/>
<key>LSMinimumSystemVersion</key>
<string>10.9</string>
<key>MinimumOSVersion</key>
<string>10.9</string>
<key>NSMainNibFile</key>
<string>MainMenu</string>
<key>NSPrincipalClass</key>
<string>NSApplication</string>
<key>NSSupportsAutomaticGraphicsSwitching</key>
<true/>
<key>ProductPageIconFile</key>
<string>ProductPageIcon.icns</string>
</dict>
</plist>
Notice the following from above:
<key>DTPlatformVersion</key>
<string>11.4</string>
<key>DTSDKName</key>
<string>macosx11.4internal</string>
That would confirm you have the actual 11.4 installer downloaded from the App Store.
Next see if the file size is way too small or not indicating you have a stub installer and not the full installer.
du -h /Applications/Install\ macOS\ Big\ Sur.app
The last line should be:
12G /Applications/Install macOS Big Sur.app
If it was a stub it would be much smaller in size than 12GB.
If all is well then you can do the following:
Format a 16GB+ USB drive via Disk Utility and name it "MyVolume" then issue the following command in Terminal
sudo /Applications/Install\ macOS\ Big\ Sur.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume
If this fails then there is something seriously wrong with your internal disk and you should verify your backups are in order then you could delete the internal drive complete and re-install Big Sur 11.4 using the USB flash drive.