Publishing to the web doesn't include private information other than the content of the file. The only one file property/meta-data that is shown in a published document is the file name.
In the Google Docs editors argot, "publishing to the web" and "sharing" are two different and independent features. The related help articles are included in the references section.
Usually the Google Docs editors official documentation mention the included features, not the missing ones.
While the published spreadsheet doesn't include any private information, this open other means of getting information of your spreadsheet but only to those that know the spreadsheet id.
The spreadsheet URL looks like this:
The spreadsheet id is
The URL of published to the web spreasheet looks like this:
AFAIK there is no way to guess a spreadsheet id, so while you keep your spreadsheet private (not shared with anyone) your private information will be kept private.
Google Docs editors Help articles