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

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

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

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

GitHub F-Droid

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)

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

I use SimpleHttp server but it's not open source and available only on play store. I use this to download epub from my e-reader after having downloaded them on my phone. Now I will look into foss solutions proposed in this Post, through termux or other apps, thanks.

Edit: indeed with termux + caddy + termux widget it's just perfect

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

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.

Does it have to be http? If FTP is ok too, you can try primitive ftpd, or the built-in FTP feature in Material Files or Amaze.