Forge Container implementation for IItemHandler

ContainerItemHandler.java

package offbeatwitch.example; // replace with your own package path, obviously

import net.minecraft.entity.player.EntityPlayer;
import net.minecraft.entity.player.EntityPlayerMP;
import net.minecraft.inventory.Container;
import net.minecraft.inventory.Slot;
import net.minecraft.item.ItemStack;
import net.minecraft.network.play.server.SPacketOpenWindow;
import net.minecraft.util.text.TextComponentString;
import net.minecraftforge.items.IItemHandler;
import net.minecraftforge.items.SlotItemHandler;

/**
 * Written by @offbeatwitch.
 * Licensed under MIT.
 */
public class ContainerItemHandler extends Container {
	private IItemHandler handler;

	private int inventoryEnd;

	public ContainerItemHandler(IItemHandler handler, EntityPlayer player) {
		this.handler = handler;
		int i = 0;

		while (i < handler.getSlots()) {
			int j = i % 9;
			int c = i / 9;

			Slot slot = new SlotItemHandler(handler, i, 8 + j * 18, 18 + c * 18);
			this.addSlotToContainer(slot);

			i++;
		}

		inventoryEnd = inventorySlots.size();

		for (int l = 0; l < 3; ++l) {
			for (int j1 = 0; j1 < 9; ++j1) {
				this.addSlotToContainer(new Slot(player.inventory, j1 + l * 9 + 9, 8 + j1 * 18, 103 + l * 18 + i));
			}
		}

		for (int i1 = 0; i1 < 9; ++i1) {
			this.addSlotToContainer(new Slot(player.inventory, i1, 8 + i1 * 18, 161 + i));
		}

	}

	@Override
	public boolean canInteractWith(EntityPlayer playerIn) {
		return true;
	}

	public SPacketOpenWindow toPacket(String type, String name) {
		return new SPacketOpenWindow(this.windowId, type, new TextComponentString(name), this.handler.getSlots());
	}

	public void open(EntityPlayerMP player, String type, String title) {
		player.getNextWindowId();
		this.windowId = player.currentWindowId;

		player.connection.sendPacket(this.toPacket(type, title));
		player.openContainer = this;
		this.addListener(player);
	}

	@Override
	public void onContainerClosed(EntityPlayer playerIn) {
		super.onContainerClosed(playerIn);
	}

	@Override
	public ItemStack transferStackInSlot(EntityPlayer playerIn, int index) {
		ItemStack stack = ItemStack.EMPTY;
		Slot slot = this.inventorySlots.get(index);

		if (slot != null && slot.getHasStack()) {
			ItemStack current = slot.getStack();
			stack = current.copy();

			if (index < inventoryEnd) {
				if (!this.mergeItemStack(current, inventoryEnd, this.inventorySlots.size(), true)) {
					return ItemStack.EMPTY;
				}
			} else if (!this.mergeItemStack(current, 0, inventoryEnd, false)) {
				return ItemStack.EMPTY;
			}

			if (current.isEmpty()) {
				slot.putStack(ItemStack.EMPTY);
			} else {
				slot.onSlotChanged();
			}
		}

		return stack;
	}
}

this is from 2018, and judging by the version history i believe it's for 1.12. i doubt this still applies to 1.13+

Container is a superset of IItemHandler - almost every container (GUI with slots) in both modded and vanilla can "handle items" i.e. has slots which handle items.
And example of a block which is a Container but isn't an IItemHandler would be some kind of liquid tank which has a GUI showing how full it is but doesn't have item slots (e.g. accept buckets).

Here is updated wrapper for 1.20.1.