Please look into Let's Go -> Sword & Shield transfer compatibility. I tried to transfer Meltan from Let's Go Eevee into Sword and this is the error code that I got, saying it is incompatible with the save file (which couldn't be true since Meltan exists in Sword & Shield):
System.InvalidOperationException: Species incompatible: 808 > 807
at PKMConverterUtils.CopyCommonPropertiesFrom(PKM pkm, PKM pkmSrc, Byte generation, PKMRndValues rndValues)
at PK7Converter.ConvertToPK7(PB7 pb7, PKMRndValues rndValues)
at PkmConvertService.TryVariantToPK(PKM source, PKMRndValues rndValues)
at PkmConvertService.TryForwardConversion(PKM source, LanguageID fallbackLang, PKMRndValues rndValues)
at PkmConvertService.ConvertRecursive(PKM current, Type targetType, LanguageID fallbackLang, PKMRndValues rndValues)
at PkmConvertService.ConvertTo(ImmutablePKM sourcePkm, Type targetPkmType, PKMRndValues rndValues, SaveFile targetSave)
at PkmConvertService.ConvertTo(ImmutablePKM sourcePkm, EntityContext context)
at MainCreatePkmVariantAction.Execute(MainCreatePkmVariantActionInput input, DataUpdateFlags flags)
at DataAction`1.ExecuteWithPayload(I input, DataUpdateFlags flags)
at MovePkmAction.MainToSave(MovePkmActionInput input, DataUpdateFlags flags, String pkmVariantId, BoxDTO sourceBox, BoxDTO targetBox, Int32 targetBoxSlot)
at MovePkmAction.<>c__DisplayClass8_0.<<Execute>g__act|0>d.MoveNext()
--- End of stack trace from previous location ---
at MovePkmAction.Execute(MovePkmActionInput input, DataUpdateFlags flags)
at DataAction`1.ExecuteWithPayload(I input, DataUpdateFlags flags)
at ActionService.<>c__DisplayClass31_0`1.<<AddAction>g__applyFn|0>d.MoveNext()
--- End of stack trace from previous location ---
at ActionService.ApplyAction(IServiceScope scope, Func`3 actionFn, DataUpdateFlags flags)
at ActionService.AddActionInner(IServiceScope scope, Func`3 actionFn, DataUpdateFlags flags)
at ActionService.AddAction[I](IServiceScope scope, Func`2 getScopedAction, I input, DataUpdateFlags _flags)
at ActionService.AddAction[I](IServiceScope scope, Func`2 getScopedAction, I input, DataUpdateFlags _flags)
at ActionService.MovePkm(String[] pkmIds, Nullable`1 sourceSaveId, Nullable`1 targetSaveId, String targetBoxId, Int32[] targetBoxSlots, Boolean attached)
at PKVault.Backend.storage.routes.StorageController.MovePkm(String[] pkmIds, Nullable`1 sourceSaveId, Nullable`1 targetSaveId, String targetBoxId, Int32[] targetBoxSlots, Boolean attached)
at lambda_method705(Closure, Object)
at Microsoft.Extensions.Internal.ObjectMethodExecutorAwaitable.Awaiter.GetResult()
at Microsoft.AspNetCore.Mvc.Infrastructure.ActionMethodExecutor.AwaitableObjectResultExecutor.Execute(ActionContext actionContext, IActionResultTypeMapper mapper, ObjectMethodExecutor executor, Object controller, Object[] arguments)
at Microsoft.AspNetCore.Mvc.Infrastructure.ControllerActionInvoker.<InvokeActionMethodAsync>g__Awaited|12_0(ControllerActionInvoker invoker, ValueTask`1 actionResultValueTask)
at Microsoft.AspNetCore.Mvc.Infrastructure.ControllerActionInvoker.<InvokeNextActionFilterAsync>g__Awaited|10_0(ControllerActionInvoker invoker, Task lastTask, State next, Scope scope, Object state, Boolean isCompleted)
at Microsoft.AspNetCore.Mvc.Infrastructure.ControllerActionInvoker.Rethrow(ActionExecutedContextSealed context)
at Microsoft.AspNetCore.Mvc.Infrastructure.ControllerActionInvoker.Next(State& next, Scope& scope, Object& state, Boolean& isCompleted)
at Microsoft.AspNetCore.Mvc.Infrastructure.ControllerActionInvoker.<InvokeInnerFilterAsync>g__Awaited|13_0(ControllerActionInvoker invoker, Task lastTask, State next, Scope scope, Object state, Boolean isCompleted)
at Microsoft.AspNetCore.Mvc.Infrastructure.ResourceInvoker.<InvokeFilterPipelineAsync>g__Awaited|20_0(ResourceInvoker invoker, Task lastTask, State next, Scope scope, Object state, Boolean isCompleted)
at Microsoft.AspNetCore.Mvc.Infrastructure.ResourceInvoker.<InvokeAsync>g__Awaited|17_0(ResourceInvoker invoker, Task task, IDisposable scope)
at Microsoft.AspNetCore.Mvc.Infrastructure.ResourceInvoker.<InvokeAsync>g__Awaited|17_0(ResourceInvoker invoker, Task task, IDisposable scope)
at ExceptionHandlingMiddleware.Invoke(HttpContext context)
Trying to transfer Melmetal gave me the same result. Additionally, when trying to transfer any other Pokemon from LGPE, their data gets jumbled up with their origin game getting changed (usually to SM/USUM or FRLG), which causes serious legality issues. This does not happen with Pokemon transferred from Gen 6 or SM/USUM, they are converted just fine with the only legality issue being the missing Home tracker (obviously). Also, when trying to "transfer" Pokemon from LGPE into SwSh via PKHeX, it works just fine, unlike in PKVault, so it looks like it's specifically a PKVault issue.