After uninstalling MySQL completely, I started getting a message from Visual Studio 2019 about a FileNotFound exception occurring while the extensions are being loaded. When I checked the logs, I saw the following snippet of XML.
When I open the Manage Extensions window, I do not see MySQL for Visual Studio listed.
<entry>
<record>781</record>
<time>2021/03/10 13:26:21.834</time>
<type>Error</type>
<source>Editor or Editor Extension</source>
<description>System.IO.FileNotFoundException: Could not load file or assembly 'MySql.VisualStudio, Version=1.2.9.0, Culture=neutral, PublicKeyToken=c5687fc88969c44d' or one of its dependencies. The system cannot find the file specified.
File name: 'MySql.VisualStudio, Version=1.2.9.0, Culture=neutral, PublicKeyToken=c5687fc88969c44d'
 at System.Reflection.RuntimeAssembly._nLoad(AssemblyName fileName, String codeBase, Evidence assemblySecurity, RuntimeAssembly locationHint, StackCrawlMark& stackMark, IntPtr pPrivHostBinder, Boolean throwOnFileNotFound, Boolean forIntrospection, Boolean suppressSecurityChecks)
 at System.Reflection.RuntimeAssembly.nLoad(AssemblyName fileName, String codeBase, Evidence assemblySecurity, RuntimeAssembly locationHint, StackCrawlMark& stackMark, IntPtr pPrivHostBinder, Boolean throwOnFileNotFound, Boolean forIntrospection, Boolean suppressSecurityChecks)
 at System.Reflection.RuntimeAssembly.InternalLoadAssemblyName(AssemblyName assemblyRef, Evidence assemblySecurity, RuntimeAssembly reqAssembly, StackCrawlMark& stackMark, IntPtr pPrivHostBinder, Boolean throwOnFileNotFound, Boolean forIntrospection, Boolean suppressSecurityChecks)
 at System.Reflection.Assembly.Load(AssemblyName assemblyRef)
 at Microsoft.VisualStudio.ExtensibilityHosting.FaultCatchingAssemblyLoader.<>c__DisplayClass17_0.<LoadAssembly>b__0(AssemblyName assemblyNameParam)
 at Microsoft.VisualStudio.ExtensibilityHosting.Utilities.SafeGetOrAdd[TKey,TValue](IDictionary`2 dictionary, TKey key, Object lockObj, Func`2 valueFactory)
 at Microsoft.VisualStudio.ExtensibilityHosting.FaultCatchingAssemblyLoader.LoadAssembly(AssemblyName assemblyName)
 at Microsoft.VisualStudio.Composition.Reflection.ResolverExtensions.GetManifest(Resolver resolver, AssemblyName assemblyName)
 at Microsoft.VisualStudio.Composition.Reflection.ResolverExtensions.TryUseFastReflection(TypeRef typeRef, Module& manifest)
 at Microsoft.VisualStudio.Composition.Reflection.ResolverExtensions.Resolve(MethodRef methodRef)
 at Microsoft.VisualStudio.Composition.Reflection.MethodRef.Resolve()
 at Microsoft.VisualStudio.Composition.RuntimeExportProviderFactory.RuntimeExportProvider.RuntimePartLifecycleTracker.CreateValue()
 at Microsoft.VisualStudio.Composition.ExportProvider.PartLifecycleTracker.Create()
 at Microsoft.VisualStudio.Composition.ExportProvider.PartLifecycleTracker.MoveNext(PartLifecycleState nextState)
 at Microsoft.VisualStudio.Composition.ExportProvider.PartLifecycleTracker.MoveToState(PartLifecycleState requiredState)
 at Microsoft.VisualStudio.Composition.ExportProvider.PartLifecycleTracker.GetValueReadyToExpose()
 at Microsoft.VisualStudio.Composition.RuntimeExportProviderFactory.RuntimeExportProvider.<>c__DisplayClass15_0.<GetExportedValueHelper>b__0()
--- End of stack trace from previous location where exception was thrown ---
 at Microsoft.VisualStudio.Composition.RuntimeExportProviderFactory.RuntimeExportProvider.<>c__DisplayClass15_0.<GetExportedValueHelper>b__0()
 at Microsoft.VisualStudio.Composition.DelegateServices.<>c__DisplayClass2_0`1.<As>b__0()
 at System.Lazy`1.CreateValue()
 at System.Lazy`1.LazyInitValue()
 at System.Lazy`1.get_Value()
 at Microsoft.VisualStudio.Text.Utilities.GuardedOperations.InstantiateExtension[TExtension,TMetadata,TExtensionInstance](Object errorSource, Lazy`2 provider, Func`2 getter)
--- End of stack trace from previous location where exception was thrown ---
 at Microsoft.VisualStudio.Telemetry.WindowsErrorReporting.WatsonReport.GetClrWatsonExceptionInfo(Exception exceptionObject)

WRN: Assembly binding logging is turned OFF.
To enable assembly bind failure logging, set the registry value [HKLM\Software\Microsoft\Fusion!EnableLog] (DWORD) to 1.
Note: There is some performance penalty associated with assembly bind failure logging.
To turn this feature off, remove the registry value [HKLM\Software\Microsoft\Fusion!EnableLog].
</description>
</entry>
When I open the Manage Extensions window, I do not see MySQL for Visual Studio listed.
<entry>
<record>781</record>
<time>2021/03/10 13:26:21.834</time>
<type>Error</type>
<source>Editor or Editor Extension</source>
<description>System.IO.FileNotFoundException: Could not load file or assembly 'MySql.VisualStudio, Version=1.2.9.0, Culture=neutral, PublicKeyToken=c5687fc88969c44d' or one of its dependencies. The system cannot find the file specified.
File name: 'MySql.VisualStudio, Version=1.2.9.0, Culture=neutral, PublicKeyToken=c5687fc88969c44d'
 at System.Reflection.RuntimeAssembly._nLoad(AssemblyName fileName, String codeBase, Evidence assemblySecurity, RuntimeAssembly locationHint, StackCrawlMark& stackMark, IntPtr pPrivHostBinder, Boolean throwOnFileNotFound, Boolean forIntrospection, Boolean suppressSecurityChecks)
 at System.Reflection.RuntimeAssembly.nLoad(AssemblyName fileName, String codeBase, Evidence assemblySecurity, RuntimeAssembly locationHint, StackCrawlMark& stackMark, IntPtr pPrivHostBinder, Boolean throwOnFileNotFound, Boolean forIntrospection, Boolean suppressSecurityChecks)
 at System.Reflection.RuntimeAssembly.InternalLoadAssemblyName(AssemblyName assemblyRef, Evidence assemblySecurity, RuntimeAssembly reqAssembly, StackCrawlMark& stackMark, IntPtr pPrivHostBinder, Boolean throwOnFileNotFound, Boolean forIntrospection, Boolean suppressSecurityChecks)
 at System.Reflection.Assembly.Load(AssemblyName assemblyRef)
 at Microsoft.VisualStudio.ExtensibilityHosting.FaultCatchingAssemblyLoader.<>c__DisplayClass17_0.<LoadAssembly>b__0(AssemblyName assemblyNameParam)
 at Microsoft.VisualStudio.ExtensibilityHosting.Utilities.SafeGetOrAdd[TKey,TValue](IDictionary`2 dictionary, TKey key, Object lockObj, Func`2 valueFactory)
 at Microsoft.VisualStudio.ExtensibilityHosting.FaultCatchingAssemblyLoader.LoadAssembly(AssemblyName assemblyName)
 at Microsoft.VisualStudio.Composition.Reflection.ResolverExtensions.GetManifest(Resolver resolver, AssemblyName assemblyName)
 at Microsoft.VisualStudio.Composition.Reflection.ResolverExtensions.TryUseFastReflection(TypeRef typeRef, Module& manifest)
 at Microsoft.VisualStudio.Composition.Reflection.ResolverExtensions.Resolve(MethodRef methodRef)
 at Microsoft.VisualStudio.Composition.Reflection.MethodRef.Resolve()
 at Microsoft.VisualStudio.Composition.RuntimeExportProviderFactory.RuntimeExportProvider.RuntimePartLifecycleTracker.CreateValue()
 at Microsoft.VisualStudio.Composition.ExportProvider.PartLifecycleTracker.Create()
 at Microsoft.VisualStudio.Composition.ExportProvider.PartLifecycleTracker.MoveNext(PartLifecycleState nextState)
 at Microsoft.VisualStudio.Composition.ExportProvider.PartLifecycleTracker.MoveToState(PartLifecycleState requiredState)
 at Microsoft.VisualStudio.Composition.ExportProvider.PartLifecycleTracker.GetValueReadyToExpose()
 at Microsoft.VisualStudio.Composition.RuntimeExportProviderFactory.RuntimeExportProvider.<>c__DisplayClass15_0.<GetExportedValueHelper>b__0()
--- End of stack trace from previous location where exception was thrown ---
 at Microsoft.VisualStudio.Composition.RuntimeExportProviderFactory.RuntimeExportProvider.<>c__DisplayClass15_0.<GetExportedValueHelper>b__0()
 at Microsoft.VisualStudio.Composition.DelegateServices.<>c__DisplayClass2_0`1.<As>b__0()
 at System.Lazy`1.CreateValue()
 at System.Lazy`1.LazyInitValue()
 at System.Lazy`1.get_Value()
 at Microsoft.VisualStudio.Text.Utilities.GuardedOperations.InstantiateExtension[TExtension,TMetadata,TExtensionInstance](Object errorSource, Lazy`2 provider, Func`2 getter)
--- End of stack trace from previous location where exception was thrown ---
 at Microsoft.VisualStudio.Telemetry.WindowsErrorReporting.WatsonReport.GetClrWatsonExceptionInfo(Exception exceptionObject)

WRN: Assembly binding logging is turned OFF.
To enable assembly bind failure logging, set the registry value [HKLM\Software\Microsoft\Fusion!EnableLog] (DWORD) to 1.
Note: There is some performance penalty associated with assembly bind failure logging.
To turn this feature off, remove the registry value [HKLM\Software\Microsoft\Fusion!EnableLog].
</description>
</entry>