You can also use Files to directly browse and access files from third party cloud services, although it requires you to download the service's app first[1].
[1] https://support.apple.com/guide/iphone/connect-external-devi...
But my use case has involved connecting to a remote host over a ZeroTier[1] VPN, using an iPhone 6S. I haven't experienced the scenario you mentioned; most problematic issue I've had is sporadic latency spikes during folder navigation. I haven't really done any true stress testing of things, but it's handled transitions between wifi and cellular network without any noticeable issues.
Looks like there are two different USB adapters Apple sells, and the product page for this[1] one mentions it can be used for quite a few USB devices, including "USB peripherals like hubs, Ethernet adapters, audio/MIDI interfaces, and card readers for CompactFlash, SD, microSD, and more."
Biggest issue for both external HDDs and other devices appears to be power delivery, which can be alleviated by using a drive with external power or leveraging a powered USB hub between the phone/tablet and the USB device.
[1] https://www.apple.com/shop/product/MK0W2AM/A/lightning-to-us...
Several apps (nPlayer, InFuse, LumaFusion) also support Samsung iXpand lightning/usb flash drives natively. With native app support, files can be played directly from the flash drive, without copying to the iPhone.