Sync gmail across apple devices

I have a gmail email account. I recently decided to setup my apple mail app to receive gmail emails. I first set it up on my mac. When I opened the mail app on my iPhone, I noticed that the corresponding mailbox was not present on the phone. So I setup the gmail account on my phone again.

After setting up both the mailboxes, I started archiving emails on my phone. However, when I went back to my mac, I noticed that nothing had changed on my mac in terms of archiving.

Since it seems like the two mailboxes are out of sync, I went into settings to make sure that the mailboxes are setup to use IMAP and they seem to be. So should I be setting up the mailboxes differently if I want them to sync across all my devices. Note that this is for my gmail account and not my icloud email.