Update
Work I've done so far:
1- Able to select users from AD and show their position, manager, and list the group membership

Combobox to find users has this code:

Filter(AddColumns(Office365Users.SearchUser({searchTerm:cmbEmpName.SearchText, top:10}) As Temp, "EmplName", IsError(Office365Users.ManagerV2(Temp.Id))),EmplName=false)
The label text for the position has this code:

cmbEmpName.Selected.JobTitle
Label for manager of the selected user has this code:

Office365Users.ManagerV2(cmbEmpName.Selected.Id).displayName
To load the groups membership of the user I create a Collection by clicking the icon Update next to the User(employee) name:

ClearCollect(AzGroupEmployee, AddColumns(AzureAD.GetMemberGroupsV2(cmbEmpName.Selected.Id,false).value, "colGroup", AzureAD.GetGroup(Value).displayName))
(Tried putting this code on the OnSelect property of the Update icon, but it doesn't work properly)
After creating the Collection, assign the values on a Gallery:

Gallery Items: AzGroupEmployee
The X next to each group is able to remove group membership for the selected user:
AzureAD.RemoveMemberFromGroup(ThisItem.Value,cmbEmpName.Selected.Id);
After removing the membership I rebuilt the Collection to update the Gallery in real time:
ClearCollect(AzGroupEmployee,AddColumns(AzureAD.GetMemberGroupsV2(cmbEmpName.Selected.Id, false).value, "colGroup", AzureAD.GetGroup(Value).displayName))
The Collection for the Employee group membership:

You wanna work with the Column Value to remove/add group membership, value is the Group ID in Active Directory.
2- Assigning new position

Basically the steps to find a new position and listing the groups are the same. What changes here is:
- On Active Directory you need to have a templates named after the positions (lets call it User-Templates) you want to have and add the groups membership to the User-Templates
- Leave every User-Template's manager field clear in AD, this way you can filter on the New Position combobox to show only the User-Templates and not all users in AD. So the code for New Position would look like this: Filter(AddColumns(Office365Users.SearchUser({searchTerm:cmbPositions.SearchText, top:10}) As Temp, "Positions", !IsError(Office365Users.ManagerV2(Temp.Id))),Positions=false)
To add a group membership to the employee I added the + icon next to the name's group for new position with this code: AzureAD.AddUserToGroup(ThisItem.Value, cmbEmpName.Selected.Id).
This is how it looks so far:

The background of the Employee's group membership (left) will be green when the employee is already member of one of the groups for the new position, and the background will be some sort of pink on the new position's group membership (right) when the employee already has this group assigned. This should avoid trying to re-assign a group. To accomplish this, I added this code to the property Fill of the control rectangle on each gallery:
For Gallery1 (containing the current groups):

If(ThisItem.colGroup exactin Gallery2.AllItems.colGroup,RGBA(10, 180, 50, .2), RGBA(0,0,0,0))
For Gallery2(containing future groups membership):

If(ThisItem.colGroup exactin Gallery1.AllItems.colGroup,RGBA(160, 10, 120, .4), RGBA(0,0,0,0))
What's next?:
- Add buttons or icons to assign new position and new manager.
- Add a button or icon to remove manager (I think this is the stone in the shoes)