Android

I just use termux + the simple http server built into python

Install termux from f-droid. Then install nginx inside termux. Works great.

I recently wanted to do the same and came upon ShareX, it did a pretty good job.

GitHub F-Droid

Sorry I don't have any suggestions, but I'm very curious about your use case. What led you to needing this?

Are you doing web dev with just a phone? Impressive

Not open source but CX File Explorer can make an FTP server for you.

Just did a search on fdroid

Servdroid looks 11 years old

LWS is about 5 which might still work

If you really need a web server you can possibly run one on termux, not sure if root required though

If its just file sharing, see the other comment

could try a flask webapp

from flask import Flask, send_from_directory
import os

app = Flask(__name__)

# Specify the directory you want to share
SHARED_DIRECTORY = 'shared_files'

@app.route('/files/<path:filename>', methods=['GET'])
def get_file(filename):
    """Serve a file from the shared directory."""
    try:
        return send_from_directory(SHARED_DIRECTORY, filename)
    except FileNotFoundError:
        return "File not found", 404

@app.route('/')
def list_files():
    """List files in the shared directory."""
    files = os.listdir(SHARED_DIRECTORY)
    files_list = '\n'.join(files)
    return f"<h1>Files in {SHARED_DIRECTORY}</h1><pre>{files_list}</pre>"

if __name__ == '__main__':
    app.run(host='0.0.0.0', port=5000)

I've been using FX File Browser for the occasional need to share stuff localy - it opens a local web server where you can browse files on the phone.
Though it's not foss and I am afraid that functionality is behind the plus version.