Example of creating UMG button and handling its on click event in C++ code

Select menu Tools->New C++ Class.... Select GameModeBase class and click Next:
Name new class "SampleGameModeBase", make it Public and click Create Class:
This step makes project C++ Project if it was created as a Blueprint one and adds class ASampleGameModeBase to it.
Close UE5 editor and open file PROJECT_DIR/Source/TestProject/TestProject.Build.cs in Visual Studio. Choose right file if you named you project any other than TestProject. Uncomment following line:
```
PrivateDependencyModuleNames.AddRange(new string[] { "Slate", "SlateCore" });
```
Save changes, recompile project by pressing Ctrl+Shift+B in VS and reopen project in UE5 Editor.

Create new class CustomButton with Object as the base class (similarly like in first step). Modify your CustomButton.h and CustomButton.cpp file to look like on following screens:

CustomButton.h

#pragma once

#include "CoreMinimal.h"
#include "SlateCore/Public/Widgets/SCompoundWidget.h"

class TESTPROJECT_API SCustomButton : public SCompoundWidget
{
	SLATE_BEGIN_ARGS(SCustomButton)
		: _Label(TEXT("Click me!"))
		, _ButtonClicked()
	{}
	SLATE_ATTRIBUTE(FString, Label)
	SLATE_EVENT(FOnClicked, ButtonClicked)
	SLATE_END_ARGS()

public:
	void Construct(const FArguments& InArgs);
	TAttribute Label;
	FOnClicked ButtonClicked;

};

CustomButton.cpp

#include "CustomButton.h"

void SCustomButton::Construct(const FArguments& InArgs)
{
	Label = InArgs._Label;
	ButtonClicked = InArgs._ButtonClicked;
	ChildSlot.VAlign(VAlign_Center)
		.HAlign(HAlign_Center)
		[
			SNew(SButton)
			.OnClicked(ButtonClicked)
		.Content()
		[
			SNew(STextBlock)
			.Text_Lambda([this] {return FText::FromString(Label.Get()); })
		]
		];
}

Create new class CustomButtonWidget with Widget as the base class (similarly like in first step). Modify your CustomButtonWidget.h and CustomButtonWidget.cpp file to look like:

CustomButtonWidget.h

#pragma once

#include "CoreMinimal.h"
#include "Blueprint/UserWidget.h"
#include "CustomButton.h"
#include "Slate/Public/Framework/SlateDelegates.h"
#include "CustomButtonWidget.generated.h"

DECLARE_DYNAMIC_DELEGATE_RetVal(FString, FGetString);

UCLASS()
class TESTPROJECT_API UCustomButtonWidget : public UUserWidget
{
	GENERATED_BODY()

protected:
	TSharedPtr MyButton;
	virtual TSharedRef RebuildWidget() override;

public:
	FReply OnButtonClicked();

	UPROPERTY(BlueprintReadWrite, EditAnywhere)
	FString Label;

	UPROPERTY()
	FGetString LabelDelegate;

	virtual void SynchronizeProperties() override;

	PROPERTY_BINDING_IMPLEMENTATION(FString, Label);
};

CustomButtonWidget.cpp

#include "CustomButtonWidget.h"

TSharedRef UCustomButtonWidget::RebuildWidget()
{
	MyButton = SNew(SCustomButton)
		.ButtonClicked(BIND_UOBJECT_DELEGATE(FOnClicked, OnButtonClicked));
	return MyButton.ToSharedRef();
}

FReply UCustomButtonWidget::OnButtonClicked()
{
	GEngine->AddOnScreenDebugMessage(-1, 5.0f, FColor::Yellow, TEXT("Button Clicked"));
	return FReply::Handled();
}


void UCustomButtonWidget::SynchronizeProperties()
{
	if (Label.Equals("")) {
		Label = TEXT("Click me!");
	}
	Super::SynchronizeProperties();
	TAttribute LabelBinding = PROPERTY_BINDING(FString, Label);
	MyButton->Label = LabelBinding;
}

To demonstrate creating custom button widget fill in SampleGameModeBase.h and SampleGameModeBase.cpp as follows:

SampleGameModeBase.h

#pragma once

#include "CoreMinimal.h"
#include "GameFramework/GameModeBase.h"
#include "CustomButtonWidget.h"
#include "SampleGameModeBase.generated.h"

UCLASS()
class TESTPROJECT_API ASampleGameModeBase : public AGameModeBase
{
	GENERATED_BODY()

	UPROPERTY()
	UCustomButtonWidget* CustomButton;

protected:
	virtual void BeginPlay() override;
};

SampleGameModeBase.cpp

#include "SampleGameModeBase.h"
#include "Blueprint/UserWidget.h"

void ASampleGameModeBase::BeginPlay()
{
	Super::BeginPlay();
	GEngine->AddOnScreenDebugMessage(-1, 5.0f, FColor::Yellow, TEXT("SampleGameModeBase!"));

	TSubclassOf ButtonClass = UCustomButtonWidget::StaticClass();
	CustomButton = CreateWidget(GetWorld(), ButtonClass);
	if (CustomButton != nullptr)
	{
		CustomButton->AddToViewport();
	}
}

Create new Blueprint class based on SampleGameModeBase:
Name it BP_SampleGameModeBase, save and set it as GameMode Override in level's World Settings. Run game to test the code and voila - the button was created, added to screen and responds on clicking it: