EXCHANGE-Online: powershell to get the number of mails in inbox not in a specific category

PowerShell can only give you the total number of items, it doesnt offer any way to filter by Category. You can easily do this in Outlook though, or if you need to do it programmatically, use EWS or the Graph API.  Here's a sample article for the former: https://gsexdev.blogspot.com/2014/10/searching-based-on-categories-in-ews.html