To display the file properties dialog on Windows 11, follow the following steps:
1: navigate to the location where the file or folder you want to view the properties of is located.
2: right click on the file or folder to display its context menu.


Alternatively: right click on an empty space in the main pane to view the context menu of the current location.

3: click on the option "Properties." The file properties dialog window will appear.

Modifying Properties
The file properties dialog is has a typical set of OK, Cancel, Apply dialog buttons. The changes won't be applied automatically. After you modify a property, e.g. by checking the Read-Only or Hidden checkboxes, you must click on OK or Apply to apply the changes.
Multiple Selection Support
It's possible to modify the properties of multiple files at once by selecting all of them before right clicking on a selected file.
Cascading Modifications
When you open the properties dialog of a folder, some settings can be applied to all descendant files and subfolders. When this happens, a dialog box will appear after you click OK or Apply asking if you want to apply the settings to only the folder selected or to the folder and its descendants.
Keyboard Shortcut
It's possible to quickly open the file properties dialog without using the mouse through the keyboard shortcut [Alt+Enter]. When this shortcut is pressed, the file properties dialog of the selected file will be opened.
Observations
In old versions of Windows, the "Properties" option of the context menu was the last item in the menu. This follows a well-established convention: in menubars of applications, File -> Properties..., Edit -> Settings..., View -> Options..., Help -> Preferences..., and similar options are usually the last or the second to last option in a submenu.
The reason for this is that the first and last items in a menu are easier to click on, since it's very easy to quickly to tell where they are the instant the menu opens without even needing to read their labels. The menu is a rectangle, so just from the contrast of the rectangle floating over a background you can tell where to click.
On Windows 11, this is no longer the case: the properties option is in the middle of the menu for some reason, and the bottom option is Show more options, which displays the old context menu where Properties is the last item.
To put it in perspective, I find it faster to click on Show more options and then click on Properties, which are both the last item in the context menu, than to try to find where Properties is in the middle of the first context menu.