Afl not having SSH access will make this more difficult to debug, but here are some leads:
I have no idea what might cause Flarum to send a 409 response, so I suspect this might not come from Flarum. Are you able to have a look at the response body of the 409 response in the Network tab of the browser dev console ?
What kind of hosting is it ? Is Flarum installed in a subfolder ? Did you use the "Customize paths" option of the installation ? https://flarum.org/docs/install.html#customizing-paths
If you moved the files to the server manually, you can run php flarum info on the local server where you generated the vendor folder.
While not necessary, can you maybe share the url of the website so we can take a look directly ?