Our HR lady took personal offence when I asked to be unsubscribed from the emails about “deals” that employees have access to from corporate partners. :(

You can set custom rules in thunderbird to deal with specific mails, like tagging it as a "sale" or just deleting it based on regex

Yeah, I ended up doing that with Outlook.

I also set up a rule to auto-delete phishing test emails based on their headers, which annoyed the security team.

Yes, the last filter is always the human being who has to deal with whatever the computer couldn't automate. But even then, you should be able to skim an email and quickly determine its relevancy, and decide whether you need to take action immediately, can leave it for the future, or can just delete it. Unless you're getting thousands of emails a day, this should be manageable.