Not any more than usual. As far as Gboard is concerned. i don't trust Google or any other closed source keyboard for that matter. i don't want it phoning home by granting it network access.
Gboard collects various types of user data to improve its features and personalize the keyboard experience. Specifically:
Typing data: Gboard collects data on the words, phrases, and characters users type to improve predictive text and spelling/grammar corrections. However, Google claims it does not retain or send any data about individual keystrokes.
Language data: It collects information on what languages users switch between to enhance multilingual typing support.
Device & account data: Basic device information and Google account details are collected for personalization and to sync settings/data across devices.
Usage data: Data on how users interact with the keyboard, what features they enable/disable, and for how long they use it each day.
While this data collection aims to improve the user experience, it does mean Gboard knows a significant amount about a user's typing habits and patterns.