The solution was that I needed to:

Import-Module Az.Accounts

before loading my modules, or within my class definition itself.

class MyClass {
    [string]$azureTenantId

    # Constructor
    MyClass () {
        #this is required        
        Import-Module Az.Accounts
    }

    [void] connectAzAccount(){
        Connect-AzAccount -TenantId $this.azureTenantId
    }

    [void] setTenantId([string]$tenantId){
        $this.azureTenantId = $tenantId
    }
}