You could put links to ChimeraX command files (*.cxc) or ChimeraX session files (*.cxs) on your web servers.  ChimeraX commands can open URLs ("open https://...") so a command file could fetch data created by the server.  The ChimeraX session files are data (in msgpack format).  Unlike Chimera 1 files which were executable Python code, the ChimeraX files are much safer (can't execute arbitrary Python).

  I am not sure if ChimeraX command and session files cover the use cases that Chimera web data files did.  Tell me if they don't.

  Another nice ChimeraX feature is that it has a built-in web browser and if you open a web page in the ChimeraX browser then special links in the page (<a href="cxcmd: open 6lu7">Open protease</a>) can execute code directly in ChimeraX.  This is a nice way to do tutorials in ChimeraX where you can click on links to run commands -- there are examples on the ChimeraX tutorials page that do this (https://www.cgl.ucsf.edu/chimerax/tutorials.html).  Potentially a user could run one of your web services from within the ChimeraX browser and then just click links on your web page to show results.  The drawback is that a user is much more likely to want to use the web browser they are used to (Safari, Firefox, Chrome, ...) since those browsers are more polished and robust.  For instance I think the ChimeraX browser can't handle logging in to password protected web sites that use a popup window.

Tom