I am trying to create a function for adding and removing a role from a user given the username (not user ID).

So far I have code that works with user ID. My question is how can I modify this code to work given the username?

const addDiscord = async (discord_username) => {
    const guild = client.guilds.cache.get('<guild-id>');   // copy the id of the server your bot is in and paste it in place of guild-ID.
    const role = guild.roles.cache.get('<role-id>');  // here we are getting the role object using the id of that role.
    const member = await guild.members.fetch('user-id'); // here we are getting the member object using the id of that member. This is the member we will add the role to.
    await member.roles.add(role);   // here we just added the role to the member we got.
}

Here is my function that will handle checking for new user to add/remove

const checkNew = async () => {
    if(toUpdate.length > 0) { // Check if there are any new users to update
        toUpdate.forEach(element => {
            addDiscord(element.new)
            // Remove element.old from Discord role
            // Add element.new to Discord role
        })
        toUpdate = []
    }
}

And here I am connecting to bot and calling the checkNew() function every 10 seconds

client.once('ready', () => {
    console.log('Ready!');

    setInterval(checkNew, 10000)
});

Update: I tried using client.users.cache.find() but it returns undefined

const addDiscord = async (discord_username) => {
    const guild = client.guilds.cache.get('<guild-id>');   // copy the id of the server your bot is in and paste it in place of guild-ID.
    const role = guild.roles.cache.get('<role-id>');  // here we are getting the role object using the id of that role.
    console.log(discord_username)
    const id = client.users.cache.find(u => u.tag === discord_username)
    console.log(id)
}

Update 2: Attempted to implement the code from Miqhtie's answer

const addDiscord = async (discord_username) => {
    const guild = client.guilds.cache.get('<server-id>');   // copy the id of the server your bot is in and paste it in place of guild-ID.
    const role = guild.roles.cache.get('<role-id>');  // here we are getting the role object using the id of that role.
    const members = await guild.members.fetch()
    const member = members.find((m) => m.username === '<discord-username>')
    console.log(member)
}

Error:

const member = members.find((m) => m.username === '<discord-username>')
                           ^
TypeError: members.find is not a function