Access to MSFS Beta but only installs Alpha!

That isn't how it works unfortunatley. You got into the Alpha from registering for the Beta (they selected a certain amount of users from the Beta for the Alpha), you weren't entitled to the Alpha, that was a bonus, you were only ever entitled to the Beta
code

So if I'm in the XCloud beta but not Alpha ring I don' have access?

I am pretty sure it is only available currently to Alpha and Beta ring in Preview. If you are in either of those rings you should be able to access the trial from inside the Hub.

There is only a limited number of free slots in Alpha/Alpha Skip Ahead.

If someone in Alpha/Alpha Skip Ahead leaves, or is removed due to inactivity, participants in Beta are invited to Alpha. However, Beta participant invitations are sent out to those, that leave valuable feedback, find bugs, and are most active in the beta
group.

So it's not how long you are in the program, but how valuable your input and bug reporting was in the past.

Added to the fact that invitations are only sent out if there is new room in Alpha, you might have to wait a while to get invited. Just provide good feedback and be patient.

Alpha trial was PC only, beta will be for everything