What you are describing seems like the expected behavior. Only certain group types are supported as members of restricted management AUs (see this table), thus ineligible entries are grayed out in the UI. In addition, said UI component only lists a limited number of entries, you cannot scroll over the entire list of groups within your organization. You can however search for individual groups by using the box on top.
In any case, if you are planning to add 500 groups as members of said AU, the UI is not the best tool for the job. The Graph SDK for PowerShell will help you automate the task, you can find examples on how to use it in this article: https://learn.microsoft.com/en-us/entra/identity/role-based-access-control/admin-units-members-add#powershell