In Calc simply clicking the cell indicator (square at bottom right) and dragging it to an adjacent cell fills the series, while Ctrl+dragging copies its content to the target cell. Unlike copy, I seldom use fill series feature, so is it possible to swap the hotkey with each other, like it is in Google Sheets?
I couldn’t find these functions in Tools>Customize>Keyboard Shortcut Keys list to swap around the hotkeys.
As another workaround to fill a range of cells with the same content, you can select a range, edit or enter the content in one cell, and accept with Alt+Enter.
To fill a selected cell range with the formula that you entered on the Input line, press Alt+Enter.
Shortcut Keys for Spreadsheets
Note (nitpicking?) to the quoted Help:
Alt+Enter happens to work in case of non-formula content (number or string) too.
You can’t reassign the mouse dragging behaviour, but instead of Ctrl+Drag you can simply copy Ctrl+C and paste Ctrl+V to a target cell (range). If the target cell is below the to-be-copied cell it’s even easier, then just press Ctrl+D to duplicate the above there, also works with a selected range / part of row. To duplicate a cell into several cells below, include the source cell in the selection and press Ctrl+D.