The plugins/ structure is designed for collections and not the role directory structure. The name of module utils in a role directory should be Ansible.ModuleUtils.Name.ps1 and it would be referenced with #AnsibleRequires -PowerShell Ansible.ModuleUtils.Name. I highly recommend using a collection though as that is what most of the documentation is geared towards.
I solved the AnsibleRequires error with the following steps:
Add ./plugins/module_utils to module_utils in ansible.cfg.
Change the AnsibleRequires line to #AnsibleRequires -PowerShell ansible.module_utils.myapplication
Next problem: The exported command is not found:
The term 'Connect-MyApplication' is not recognized as the name of a cmdlet,
function, script file, or operable program. Check the spelling of the name, or
if a path was included, verify that the path is correct and try again.