I use x-plore, whilst not open-source, it hasn't had too many issues with privacy-related annoyances and a tcpdump on the router doesn't show it doing anything untoward.
This brings back memories of a really old Nokia that I had around 6-7 years back. There was this 3rd party file browser called x-plore that had this feature for multiple file selection. It seemed so simple and intuitive at that time, blew the native file browser right out the waters. Along with easily the greatest 3rd party app selection (of that time) and built-in multitasking (in 2007!!), Symbian and Nokia ruled in those days!
edit: Found the app link explaining this feature! http://www.lonelycatgames.com/?app=xplore&page=symbian/manual
I've been using X-plore since my Nokia Symbian days and really like it. I use SMB in its dual-pane directory interface for file operations over home wifi but FTP and other protocols are also built in. Find it on Google Play store - it's free! 🔝(You're welcome.)