After full rewrite, I split the plugin, and now it works on both Spigot and BungeeCord. Since BungeeCord edits packet sent from server, to remove Bungee version prefix you need to install plugin on your BungeeCord. More description about how it works now you can find below.

If you only have plugin on your bungee server, it will edit server brand on every server in your network. You can exclude servers, where you don't want to edit it. Groups are determined by BungeeCord config, or LuckPerms if installed.
If you have plugin on BungeeCord and plugin on Spigot server, they'll hook into each other, and removing BungeeCord version prefix. If you set `bungee-as-primary` on your Spigot server, BungeeCord takes control over plugin and sends messages from own config. It allows using of Vault and PlaceholderAPI from BungeeCord.
If you enabled `api-only` in Bungee plugin config, BungeeCord not sending any messages, and only used by plugins on servers. (servers without F3Name will have standar server brand)

This stuff is quite complicated, so errors are possible. You're welcome to discussion thread if you have a problems.