Element is not a solution, it is a client. Matrix is the protocol. Discord happens to provide both in a spectacularly privacy disrespecting way imo.
I know of two chat protocols which are quite popular: matrix and xmpp. Matrix seems to be the more flashy but also more energy consuming part. Xmpp is very old and apparently has been EEEd by google at some point which is the whole reason matrix exists imo.
As clients go, you can use one of dozens of them, each different. Element (and element x) are made by people who also are involved with matrix but run a for profit company as well so beware. They also make contributors sign away their rights if they ever wanted to take element closed source which is a red flag.
I mostly use fluffychat which isnt perfect but works very well imo. I also have bridges on my matrix server (i use synapse) which connect whatsapp, signal and discord for the folks who dont want to switch over but want to talk to me. This makes is convenient for me and I still have encryption and control over my data in the pure matrix chats.
I cant comment on running xmpp bc no experience but reports say its very fast. Running your own matrix server or using a known host means you have no ads, no tracking, e2ee and you will likely always know where your data goes.
Thanks for reading and have a good one.