If you simply installed Postfix, but didn't configure it fully or properly, about the only thing it'll be good for out of the box is sending mail locally. External mail will almost always land in the SPAM/Junk bin (i.e. any mail sent to Google, Yahoo, [insert provider]).
When it comes to Postfix, you really need to setup a working mail server and that mail server ideally needs to be on it's own Droplet/VPS/Dedicated, separate from applications, web-based or other.
You also really need to setup SPF, DKIM, DMARC, Black/Grey Lists, Spam and AV, etc. If that sounds like a pain, it's because it really is. I've worked with Linux for over 15 years and I still dread setting up mail servers, even if the script I'm using fully automates the process. It's the constant work required after the setup that's where the pain points are, not really the initial setup.
That said, when it comes to using external services, such as MailGun, Zoho, etc, are you seeing any sort of error? Are you just not receiving the e-mail, is it landing in SPAM/Junk, bouncing, etc?
Even with these services (i.e. MailGun, SendGrid, etc), you still need to run through their process of setting up SPF and DKIM through their services (which is done through their control panels), else mail will still land in the SPAM/Junk bin.