Per https://support.symantec.com/en_US/article.TECH193686.html, there is no setting in SEPM to control the timeout of the SEPM web console. As instructed in that tech article I am making an official request to add this option.
I use Chrome and as documented there is no way to control this with this browser. Further I would not want to set that on a browser wide basis, for security reasons. As such it makes sense to control this within the SEPM product itself.