Matrix allows you to structure rooms pretty similar to Discord. It's called a "space" that can then have rooms. Also Sub-spaces with more rooms. You can then manage access by inheritance or really granular on a space / room level. E.g. hidden / public rooms and spaces.

A few notes though:

• If you can create a space / room might depend on the Matrix server you are on and what capabilities the server admin gives you.
• There is always the option to completely self-host your Matrix instance - like Lemmy, Mastodon, etc. Depends on how tech savvy you are and if self-hosting is worth it to you ( can mean a ton of work).
• I am not claiming Matrix is a full on Discord replacement. Discord has it's advantages, but so does Matrix if autonomy, privacy, security are important to you. Matrix does have also neat features and bot-ability... but it's clearly not as easy as Discord. Good enough for many FOSS projects / communities though.
• IMO one key concept (besides decentralization / federation) that can be hard to grasp for new users is the concept of the recovery key that you get in addition to your username / password. Also does not help that there is "legacy" Element and Element X which add some confusion as they differ a bit in functionality.
• Personally I really like Matrix. Cinny might be an alternative client that might appeal more to you than Element. If you are into self-hosting tuwunel might be worth a look (or matrix synapse if you want to go with the OG server implementation)