If you're using the + trick, you haven't gained any privacy, because I can strip the + and get your original address.
If you're using a catch-all domain, you haven't gained any privacy, because the domain remains a unique identifier for your all of your accounts. It's good for organizing, but not for privacy, because you're still publicly attaching your identity to every email you send.
With fastmail, I don't need to do [email protected] or [email protected]. I can just do [email protected]. That's a really large privacy win, since it gets rid of one of the biggest and least regulated unique identifiers that services can share with each other.
I don't know if other providers like Outlook are also offering 'real' aliases. I'm happy if they are, I think this should be an industry standard feature. Either way, switching to any provider does will be a pretty significant feature upgrade over Gmail, even if you're currently using a paid Gmail account with your own domain.
So It so different from random domain catchall?
The reason why i would be worried about Fastmail is that they have are Australian company with servers in US. Both of those mean that Law enforcement can simply ask for users emails.
Now i am for sure not target of Law enforcement or goverment so i dont care but i am not sure why i wouldnt use service thats in better juristiction and is privacy focused.
With some you can do the + trick (which gmail probably still does) but i just have my domain as catchall and it works pretty great with blacklisting.