I spent quite a bit of time figuring out why this plugin often throws an error (leaving a .tif file and aborting the export) and found a 100% working solution. Below is a step-by-step guide that will save you hours of Googling and experimenting with your computer.
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Important Notice: The steps below involve changing system environment variables (Windows). Please follow the instructions very carefully. By proceeding, you agree that you are doing this at your own risk. The author assumes no liability for any damage or software conflicts.
We will need two free files: the plugin itself and the official encoder from Google.
WebP Export Plugin (by Marco De Maio)
Source: Author's Official Website
Scroll down to the Download section and download the ZIP archive with the plugin (it will contain a .lrplugin folder).
Official cwebp Encoder (by Google)
Source: Google WebP Libraries Repository
Find and download the stable version for Windows in the list (the file is named libwebp-X.X.X-windows-x64.zip; choose the latest version without the rc prefix).
The program from Google does not require installation, but it needs a proper location on your computer.
Extract the downloaded Google archive (libwebp...zip).
Open the extracted folder, find the bin folder, and copy only one file from it – cwebp.exe.
Create a new folder on your C:\ drive with a simple name (for example, C:\WebP\) and paste the cwebp.exe file there. Important: the folder path must contain only English letters, with no spaces or dots!
Note: If you skip this step, the plugin in Lightroom will likely throw an error and leave a temporary .tif file. We need to teach Windows to "see" the encoder program.
Click the Start menu and type "Edit the system environment variables". Open this section.
At the bottom of the window that opens, click the "Environment Variables..." button.
In the bottom list (System variables), find the Path row, select it, and click "Edit...".
Click "New" and type the path to the folder where your encoder is located (for example, C:\WebP).
Click OK in all windows to save the changes.
Extract the archive with Marco De Maio's plugin. Move the folder with the .lrplugin extension to a safe place (for example, to your "Documents" folder or wherever you keep your presets).
Open Lightroom Classic.
In the top menu, select File -> Plug-in Manager.
Click Add in the bottom left corner and select your .lrplugin folder. The plugin will appear in the list with a green "Installed and running" indicator.
Now you can export WebP files in batches!
Select your photos and click Export.
At the very top of the window, in the Export To drop-down menu, select our new plugin – WebP.
Scroll down the settings window to the very bottom to the WebP section.
Critically important: Leave the Path to cwebp field completely blank! (Since we configured the system in Step 3, the plugin will find the program itself).
Quality: Set it to 75–80. The human eye won't see the difference from 100%, but the file size will be perfect (150–300 KB for a photo 1200px wide).
Click Export and enjoy the speed!