result = re.search('(.*) On (.*), (.*),(.*) at (.*)', m['snippet'])

result.group(1): RELEVANT MESSAGE On Thu, Apr 25, 2019 at 10:34 AM Some Name <some@email.com> wrote: QUOTED MESSAGE
result.group(2): On Thu, Apr 25, 2019 at 10:33 AM <some_other@email.com> wrote: PREVIOUS QUOTED MESSAGE

result.group(1): RELEVANT MESSAGE
result.group(2): On Thu, Apr 25, 2019 at 10:34 AM Some Name <some@email.com> wrote: QUOTED MESSAGE On Thu, Apr 25, 2019 at 10:33 AM <some_other@email.com> wrote: PREVIOUS QUOTED MESSAGE

result.group(1): RELEVANT MESSAGE
result.group(2): On Thu, Apr 25, 2019 at 10:34 AM Some Name <some@email.com> wrote: QUOTED MESSAGE
result.group(3): On Thu, Apr 25, 2019 at 10:33 AM <some_other@email.com> wrote: PREVIOUS QUOTED MESSAGE