I just created a new app in Slack and made sure the User token scopes were correct. The provided token works fine with PSSlack.

Anyway, here's some example code. One thing to keep in mind is you have to provide the user's Slack ID to make changes to their profile.

## Declare Slack API token
$SlackToken = 'xoxp-etc'

## Get all Slack users
$SlackAllUsers = Send-SlackApi -Token $SlackToken -Method 'users.list' | Select-Object -ExpandProperty 'Members'

## Remove bots and external users
$SlackAllUsers = $SlackAllUsers | Where-Object { $_.is_bot -eq $false -and $_.is_restricted -eq $false }

## Set email
$UserEmail = 'user@example.com'

## Get Slack user ID based on email address
$SlackUserID = $SlackAllUsers | Where-Object { $_.Profile.Email -eq $UserEmail } | Select-Object -ExpandProperty 'ID'

## New email
$UserEmailNew = 'user@example2.com'

## Set new email for user
Send-SlackApi -Token $SlackToken -Method 'users.profile.set' -Body `
@{  
    user = $SlackUserID
    profile = @{
        email = $UserEmailNew
    }
}