Is there a way to automatically move data using a formula?
But in order to be more helpful in any kind of specific way--since in fact there are several ways to use formulas "to automatically move data" to some kind of summary page or (as they're often called in Excel circles) a dashboard tab--you'd help us help you be giving a more complete picture of what you're working with.
In the absence of that, let me refer you to the FILTER function and this video, on YouTube, that Microsoft used to introduce the FILTER function. If what you have is a relatively normal Excel table, with dates and various text fields arrayed in columns corresponding to those dates, the FILTER function may well be exactly what you need.
If that doesn't work--by the way, FILTER does require Excel 2021 or newer, or a Microsoft 365 subscription--then come back with a more complete description of what you have. Ideally, if the data aren't confidential, post a copy of your workbook on OneDrive or GoogleDrive, with a link pasted here that grants access to it.