Open Source

Is there a file transfer app that could transfer a file directly to a nearby

I don't think there's anything exactly like Apple Airdrop. Apple's airdrop uses a combination of bluetooth to find nearby devices, and a temporary wifi link to send them. It's a custom protocol, that only works because Apple controls the hardware, firmware and software, whereas on nonrooted android phones you simply don't have that level of control over the devices.

In addition to that, many wifi adapters only support being in one "mode" at once, so they are unable to be simultaneously connected to a network, and connected to another device via a direct conenction. Apple gets around this via hardware control, where they can ensure that all their devices, essentially have two wifi adapters inside them.

If you want an alternative to just send wifi files without an internet connection however, bluetooth supports sending and receiving files. Although, bluetooth is much slower than wifi, and you will have to pair the devices first.

EDIT: it looks like a commenter above has claimed that apple devices don't support bluetooth file transfer. So an alternative you could consider is bluetooth tethering, where you connect to a wifi network hosted over bluetooth, and then send files through there. But this requires even more setup, and I dunno if Apple devices support this as well.

LocalSend actually works without internet - it just needs both devices on the same local network (one phone can create a hotspot for the other to join if you're completely offline).