Categories in OWA

You're welcome.

My opinion is that the sync issue might be caused by Outlook for Mac, not OWA. You could try the following steps (https://support.office.com/en-us/article/I-m-not-receiving-email-or-other-items-in-my-Exchange-account-in-Outlook-2016-for-Mac-d47b51ce-e0ee-4c5f-bbc3-e0b98dec39e9):

Cause: Items from an Exchange account are stored in the Outlook cache. If this cache becomes corrupted, it may cause synchronization problems with the Exchange server.
Solution: Empty the cache in Outlook so that Outlook can download all the items from your Microsoft Exchange account again.

CAUTION: The following procedure deletes any information that is not synchronized with the Exchange server, including your contacts' mail certificate. Emptying the cache replaces the contents of the folder with the latest items from the Exchange server. Before emptying the cache, you may want to ensure that your Outlook information is backed up.

1. Make sure that your computer is connected to the Exchange server.
2. In the navigation pane, Ctrl+click or right-click the Exchange folder for which you want to empty the cache, and then click Properties.
3. On the General tab, click Empty Cache.
4. After the folder is empty, Outlook automatically downloads the items from the Exchange server.

I understood that you are not importing or migrating anything. I gave you that info because there is an important part there, "Outlook 2016 for Mac uses the Master Category List (MCL) that is stored on the Exchange server to synchronize the category names and colors".

What this means is that the categories visible in Outlook for Mac are the same ones as those visible in OWA, so you should be able to apply then using one client and see them in the other client, unless there is a synchronization issue.

A bit of info about categories in Outlook for Mac:

https://support.microsoft.com/en-gb/kb/3009176

Outlook for Mac 2011 uses a local list of categories. The names of these categories are synchronized to the server that is running Microsoft Exchange Server when they are assigned to items. This makes the names visible on different clients and devices. However, the colors for these categories aren't synchronized to Exchange.

Outlook 2016 for Mac uses the Master Category List (MCL) that is stored on the Exchange server to synchronize the category names and colors.

Therefore, when you migrate from Outlook for Mac 2011 to Outlook 2016 for Mac, any local category names that are assigned to items are merged with the MCL. Random colors are assigned to these categories because the colors from Outlook for Mac 2011 are not synchronized.