I am a beneficiary of an H-1B petition filed by an U.S. employer, and I am now in my 60-day grace period following the end of my OPT employment authorization. 

May I benefit from an automatic status extension? If yes, would I be able to continue employment? or will it just extend my grace period until the October 1 employment start date?

The H-1B petition requesting for change of status has to be timely filed, which is defined as filing before your current nonimmigrant status expires. In addition, the duration of status while on OPT is defined as including the 60-day grace period. Furthermore, the USCIS rule also states that any employment authorization is extended if an H-1B petition is timely filed. 

Based on USCIS rule, if an H-1B petition with change of status is timely filed before your current F-1 status expires, then you may be able to take advantage of both the automatic extension of status and the automatic extension of employment authorization.