Having the same issue , with installing ipadOS 15 , Have successfully installed the beta profile , restarted my device , the update shows up under software update . But the download button is greyed out , and it says wifi is required to download this update .
Nothing i do seems to fix this , have turned on and off , auto download and install updates , have tried deleting the profile and re- downloading it . But nothing seems to work so far . I use an iPad Air 2019 running on ipados 14.6