Discord has 5 levels of user verification.
None.(none)
Verified email. (Low)
Verified email + more than 5 minutes old account. (Medium)
Verified email + >5 mins old account + member of server for more than 10 mins. (High)
Verified email + >5 mins old account + server member >10 mins + verified phone number. (Highest)
Server admins can set the level. Some server sizes or types (community severs etc.) have a discord-mandated minimum level to qualify for the server type.
Normally (Medium) or (High) security is more than enough. Servers that experience raiding or high levels of trolling are recommended to choose (Very High) security as it makes it harder to make multiple accounts and evade bans or brigade a server.
Discord store the number. The server never sees those details.
Servers that ask for ID to ensure you are over age, are doing that in their own, and probably illegally handling that data, without adequate security.
The server sets the security level. Discord does the enforcing. It IS discord asking for the phone number. But only because the server asked Discord to. But the server definately doesn't see your phone number.
I run a game community server, and normally have security set at medium.
If raided, it goes to High.
If persistently trolled by a user or users that are ban evading (has happened only once), I turn it to highest for a bit.
But I turn it back down after a bit.
A bigger server might not get that luxury.
If a server has stupid high security settings, chances are they have active troublemakers.
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Laughs in ADHD