1. Adobe Premiere Pro User Guide
"Split or cut one or more clips" section.
Under the subsection "Split clips using the Razor tool
" the documentation states: "To split all clips on all tracks at a specific point
select the Razor tool and Shift-click at that point." This directly confirms that holding Shift with the Razor tool performs a "through edit."
Source: Adobe Inc. (2023). Premiere Pro User Guide. Retrieved from https://helpx.adobe.com/premiere-pro/using/trimming-clips.html#split-or-cut-one-or-more-clips
2. Adobe Premiere Pro User Guide
"Default keyboard shortcuts in Premiere Pro" section.
The documentation for the Razor tool (C) describes its basic function. The modification of this tool's behavior with the Shift key is a core feature. The alternative keyboard shortcut Control+Shift+K (Windows) or Command+Shift+K (macOS) performs a similar function ("Add Edit to All Tracks")
but the method described in option C is the correct one involving the Razor tool itself.
Source: Adobe Inc. (2023). Premiere Pro User Guide. Retrieved from https://helpx.adobe.com/premiere-pro/using/default-keyboard-shortcuts.html