GuildMemberUpdate's oldMember doesn't have correct roles.

const { Events } = require('discord.js');
require('dotenv').config();

module.exports = {
  name: Events.GuildMemberUpdate,
  async execute(oldMember, newMember) {
    console.log(oldMember.roles.cache); //oldMember only has @everyone role
    console.log(newMember.roles.cache); //newMember correctly has 3 or 4 different roles depending on whether the role was just added or removed.
    if (
      !(
        oldMember.roles.resolve(process.env.GREETER_ROLE_ID) ||
        newMember.roles.resolve(process.env.GREETER_ROLE_ID)
      )
    ) {
      console.log("Event doesn't concern greeter role"); // This gets run if the member isn't cached but the correct role was removed.
      return;
    } else {
      console.log("Event concerns greeter role") //After removing the role and adding it back this will be run every time from now on
    }
  },
};

const { Events } = require('discord.js');
require('dotenv').config();

module.exports = {
  name: Events.GuildMemberUpdate,
  async execute(oldMember, newMember) {
    console.log(oldMember.roles.cache); //oldMember only has @everyone role
    console.log(newMember.roles.cache); //newMember correctly has 3 or 4 different roles depending on whether the role was just added or removed.
    if (
      !(
        oldMember.roles.resolve(process.env.GREETER_ROLE_ID) ||
        newMember.roles.resolve(process.env.GREETER_ROLE_ID)
      )
    ) {
      console.log("Event doesn't concern greeter role"); // This gets run if the member isn't cached but the correct role was removed.
      return;
    } else {
      console.log("Event concerns greeter role") //After removing the role and adding it back this will be run every time from now on
    }
  },
};

const client = new Client({
  intents: [
    GatewayIntentBits.Guilds,
    GatewayIntentBits.GuildMembers,
    GatewayIntentBits.GuildMessages,
    GatewayIntentBits.MessageContent,
  ],
  partials: [Partials.GuildMember],
});

const client = new Client({
  intents: [
    GatewayIntentBits.Guilds,
    GatewayIntentBits.GuildMembers,
    GatewayIntentBits.GuildMessages,
    GatewayIntentBits.MessageContent,
  ],
  partials: [Partials.GuildMember],
});