Cloud services are not exactly private.  I am pretty sure there are some selfhosted options out there that would do this.
Could you not just find an email client you like, that does complex rules (ie thunderbird) and run it on a pc (or rasbertyPI)?
It might not be instantaneous, but I think it would work.

Thunderbird also has a portable app. Not sure if its rules are up to what you are looking for. 

Worrying about portable later makes sense. I will try and run it tonight when I get home, but it will be pretty late. Otherwise I might not get to it until tomorrow.
Hope that does not delay you to much.
Thanks

Thank you. The first ALPHA version should be coming up. I'm running an Ubuntu-based distro (20.04) so it might as well be Linux since I'm using it with good results.

Thats great. I have Linux Mint.

Puppeteer programming is logical and I'm confident this is the way forward since basically all the sites & webmasters account for Chrome/Chromium. The only complaint is the ~400MB overall release package size but we'll cope with it.

That is pretty large, but totally doable.  You had mentioned it being portable. So I am assuming if need be I could run it off of an external USB 3.0 or more.