AttributeError: 'CogLoader' object has no attribute '_BotBase__extensions'

You need to initialize the commands.Bot in your CogLoader.__init__

This can be accomplished through the following code:

class CogLoader(commands.Bot):

    def __init__(self, command_prefix, **options):
        super().__init__(command_prefix, **options)
        for filename in os.listdir('./cogs'):
            if filename.endswith(".py"):
                try:
                    self.load_extension(f"cogs.{filename[:-3]}")
                except Exception as e:
                    print(f"cogs.{filename[:-3]} cannot be loaded")
                    raise e

and

def main():
    bot = CustomBotClient(command_prefix="!")

This way, commands.Bot and BotBase, their attributes and their methods are loaded.