I lived in Switzerland for a few years as a kid and used to love Schaffhausen's Fasnacht. I'd actually totally forgotten about it until seeing this post!
One thing I do, which no clue how helpful it really is, is use a custom domain for my emails with support for catch-all addresses. When I sign up for a new site, I typically put my email as something like "<site-name>@<my-domain>.com".
If my data were exposed, I guess someone who realized that could try any variation of the site's name to figure out the exact one in my address, but you could always do something more unique than that. Even something like generate a BitWarden password and use it as the user for the domain.