IOS – Is Notes sync broken on iOS 14 and macOS Mojave 10.14

iOS Notes only supports syncing with iCloud or an IMAP email account, according to their Syncing Notes support article.

If your Exchange server allows IMAP access, you could create another account on your iOS device that only syncs the notes for your account. You'll have to ask your Exchange admin whether they have enabled IMAP access and what the settings are for it.

There are a handful of iOS apps which claim to sync Exchange notes, but their reviews indicate that they're unreliable, and it doesn't appear that any of them support Exchange 2010 or 2013. As of this writing, the IMAP workaround appears to be the best option.

It's a bit difficult to diagnose this with the info you've given but from experience I've found that you are able to reliably "force an sync" with any sort of iCloud data by going to System Preferences and signing out + signing back in (it'll warn you about removing iCloud data from the device, etc.)

As said in the previous answer, make sure you are syncing your notes with iCloud and not with a) another provider (Google, Exchange) or b) not syncing at all (i.e., storing locally). Verify this on the iPhone in Settings > Notes > Accounts or on the Mac with System Preferences > Internet Accounts.

The best way to see what is actually being stored in iCloud is at its web app like you've been doing.