How do I connect my app to chat?

Your code appears to be correct, since you are using .env and your config object looks similar to the example on the tmi.js quick start.

You did preceed your password with oauth:

Are you getting errors?

const client = new tmi.Client({
	options: { debug: true, messagesLogLevel: "info" },
	connection: {
		reconnect: true,
		secure: true
	},
	identity: {
		username: 'bot-name',
		password: 'oauth:my-bot-token'
	},
	channels: [ 'my-channel' ]
});

Is the example from tmi.js