@lookingforward wrote
True, Amtrak does service the Newark airport station directly. However not every Northeast corridor Amtrak, nor the Acela stops at the airport station. Newark Penn station is only a 5 min ride away from EWR station. Depending on the time of day, the person might be stuck waiting at EWR for the next Amtrak for 2+ hours. It would be far easier to take the NJ Transit to either Newark Penn Station or NY Penn Station and then take the next Amtrak to New Haven.
For details, see the full schedule here.
https://www.amtrak.com/content/dam/projects/dotcom/english/public/documents/timetables/Northeast-Schedule-W04-030419.pdf