Given that there hasn't been any development on this plugin for two years (refer to Lightweight Social Icons on WordPress), I've taken the initiative to update it. I've introduced a newer version of Fontello (the font used in the plugin) to include Mastodon and Telegram. Additionally, I've removed Google+ since it's now defunct.
To update, simply replace the original plugin files in your WordPress installation using FTP. This ensures you retain all your configurations. After this, you'll be able to add the newly introduced social networks.
If you'd like to request new icons, please open an Issue. In the "asset" folder, I've also provided a JSON configuration file. You can upload this to Fontello to view the hex codes of the icons, modify them, add more, and so on.
Should you have any questions, please don't hesitate to contact me.
Credits:
https://generatepress.com/forums/topic/lightweight-social-icons-request/#post-172570