In order to have a eagler server you need a VPS service, Dedicated Server or a Selfhosted Server
There is no official host that Eaglercraft uses!
A few recommended VPS (and dedicated host) services are listed below (but keep in mind these are not the only options):
Dollar Dollar Nodes (https://ddnodes.com)
Hetzner (https://www.hetzner.com/cloud/)
Q-FI (https://qficloud.com)
FiberState (https://www.fiberstate.com/#deals)
ABR Hosting (https://abrhosting.com/)
You could use Github Codespaces or Repl.it, however, it is highly discouraged for many reasons such as having security concerns and that free resources are limited which can limit your ability to list your server on Eagler Server List.
Please note that if you use another host (especially popular Minecraft hosts and VPS providers), you must make sure it will work with Eaglercraft.
For example, some hosts don't allow installing custom plugins such as EaglerXServer.
Also note that getting SSL to work (for wss://, required for any client that is not an offline download) is even harder as most game hosts don't natively support web connections or allow running other software such as CertBot (for SSL certificates), Cloudflared (a web tunnel, requires paid Cloudflare domain, also has SSL), or Ngrok (web tunnel with SSL). You may have better luck on dedicated servers or non-gaming hosting providers (oddly enough).