You can connect FastMail to gmail and never look at gmail. Your employer may not approve if you hillary your emails like that though, but that's what I did at a previous employer where this wasn't an issue.
You're still using gmail's spam checking; it just uses the API (or IMAP? I forgot) to sync the emails to FastMail.
[0]: https://www.fastmail.com/blog/fastmail-snooze/
Edit: If you want your work emails to arrive only during work hours and otherwise delay them, you can use a Sieve condition in your email rule similar to this:
anyof (date :value "lt" "date" "hour" "09", date :value "ge" "date" "hour" "17")LOL