How can I share a .style so that the same symbology can be used by others in my organization (Desktop 10.7.1)?
Your personal style is stored in the folder <install drive>:\Users\<username>\AppData\Roaming\ESRI\Desktop10.7\ArcMap. You can copy this file to a network share that other users can load into their system from Style References Dialog and use this in their projects via the Add Style to List.
The ESRI styles are stored in <install drive>:\Program Files (x86)\ArcGIS\Desktop10.x\Styles which can also be copied, renamed and saved in a shared network folder to be added in as well
Please also take a look at Creating new styles - ArcGIS Desktop.