I keep hearing human sighs on Minecraft

It may be a ghast, either in the nether, or it escaped through a portal (I am not sure if they can do that, but if they can, then that would be possible).

Turn on subtitles and look what they say while you hear that sound, to turn on subtitles go to the settings, "Options...", "Accessibility settings...", "Show Subtitles".

Try if you can hear it in every dimension (overworld, nether, and end).

Try if you can hear it in peaceful mode.

I'm not the only one, it seems. I heard it about five minutes ago while on a Realm.

Do note that I have not played Minecraft for a very long time and only recently started playing again. In fact, the last version of Minecraft I played was around version 1.7 or so.

Anyway, after doing a little bit of research, I stumbled upon Ambiences. Take a look at the following link and expand the list.

https://minecraft.gamepedia.com/Ambience#Cave_ambience

My guess is that what we had heard is Cave 4, but played from extremely far away and/or softly.