Am I required to report an incident that isn't specifically mentioned in 49 CFR 830?
There are a couple of part 91 regulations that require 'general' incident reporting, but only if the FAA or ATC requests it.
14 CFR 91.3(c) says that if a pilot exercised emergency authority to deviate from part 91 rules then the FAA can ask for a report:

(b) In an in-flight emergency requiring immediate action, the pilot in
command may deviate from any rule of this part to the extent required
to meet that emergency.
(c) Each pilot in command who deviates from a rule under paragraph (b)
of this section shall, upon the request of the Administrator, send a
written report of that deviation to the Administrator.

91.123(d) says that ATC can ask for a report if they gave a pilot emergency priority, even if the pilot didn't deviate from any rules:

(d) Each pilot in command who (though not deviating from a rule of
this subpart) is given priority by ATC in an emergency, shall submit a
detailed report of that emergency within 48 hours to the manager of
that ATC facility, if requested by ATC.

There are also regulations for charters (135.415) and airlines (121.703) that have a long list of &quot;service difficulties&quot; that must be reported, including in-flight fires, brake failures and others. And there are likely non-FAA regulations on things like HAZMAT incidents.