You can use Nextcloud for this. There are providers offering a few GB for free, like the Germany-based Webo or Swiss-based Wölkli, both offering 3GB storage in their free plans.
Nextcloud file storage can be mounted locally using WebDAV, which is easily done on a Linux machine, no additional software needed, only a single line added to
https://<Nextcloud-Server>/remote.php/dav/files/<user>/ /home/<user>/dav davfs user,rw,noauto,_netdev 0 0
(of course you can use a divverent mount point, so this is just an example line. Important parameters are
user (so you can mount it without root),
rw for read and write access,
_netdev telling the system this cannot be mounted before the network is up).
That done, your backups are placed on the server by simply copying it to the locally mounted Nextcloud folder. Let's see how it matches your requirements altogether:
- Runs as a Linux service (daemon / bg job) that monitors files in a specific directory. I will have a cron job that adds files into the monitored folder periodically: Not exactly (no Linux service), but the goal is still reached: all files placed there end up on the server.
- Has a Web App / Web API where I can easily check that the files are being uploaded daily and they are easy to download: Yes, you can check that via your browser on any device supporting a browser (see screenshot below). If it were an Android device, you could even use their app for it (but then, this would also take care for/mirror the files).
- Is free up to some limit (100MB is more than enough): You'll get 3GB with the services mentioned. So it's 30 times more than enough :)
- Is not self hosted. I want to avoid having to make a backup of the backup.: You can self-host it (and then available storage is up to you). But as you do not wish to, see above – there are services available from multiple places. Backup of the backup included.
Nextcloud Files in a web browser. Source: Nextcloud. As you see, you can even comment on files.
I'm using Nextcloud myself (self-hosted) and can say it works relyable and IMHO perfectly fits your use-case. Using the hosted variant you'd even not have to care for updates, so it should be a hassle-free experience. Once set up, it simply works.