The current version of Columnal runs locally on your machine. This means that the data never leaves your computer, and thus Columnal does not transmit any of the data that you load into it; it is only stored locally in the Columnal files that you save.
Columnal does collect some usage statistics and reports these to its central server, along with information about any internal errors (which should be very rare). These statistics do not contain any user data. The statistics include things like number of projects opened, number of times interface features, transformations or library functions are used, and so on. They are not tied to any identifying data.
The Columnal website does not contain any adverts or detailed tracking. We use simple tracking to count pageviews, unique visitors, referrals and country data. None of this data is tracked to any identifying data and it is only used for internal analytical purposes. It is not resold and it is not linked to any data about using the actual software.