Bridge gallery

You can create Web Galleries in Lightroom (Web Module)

Bridge Output module is an optional download these days.  You need to download and install it.  You may als need one of the older Bridge versions for Web Gallries.   Bridge CS6

My Bridge CC  output module does not seem to be functional ?

Re downloaded Output Module and re install it fix Bridge CC  output module.

Bridge CC 2018 Output module only seems to output PDF.

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Adobe Output Module for Bridge CC 2018 version 8.0

Beginning with the October 2017 release of Bridge CC, the following updates have been made:

• A new Output workspace has been introduced to generate PDF contact sheet natively in Bridge. You don't need to install Adobe Output Module separately. For help documentation, see Create a PDF contact sheet in Output workspace.
• The Adobe Output Module (AOM) plug-in (explained in this article) is no longer supported and the functionality to create web galleries has been discontinued in the latest version of Bridge.
• The Adobe Output Module (AOM) plug-in works only with Bridge CC 2017 (version 7.0) and earlier releases. You can download the appropriate AOM file using the links provided in this article.

All version cam be found here  How to install Adobe Output Module in Bridge CC

There are some Photoshop Scripts the can create Web galleries on the web.