[nitrogen]

Since Gmail's account name semantics are well known, the top data collecting agencies have no doubt adapted by now.

Also, frustratingly, a lot of sites will break, often silently, if you give them an e-mail address with a plus symbol (e.g. it might end up in a GET request to an internal API without proper escaping, and be interpreted as a space).

[Amadou]

Yes, the only way to go is your own domain. Use an add-on like Virtual Identity for Thunderbird to keep track of which From address goes with which recipient. https://www.absorb.it/virtual-id (their cert seems to have expired over the weekend)

[Evbn]

I do wonder when/if trackers collapse all addresses on a small domain into a glob. They totally could.