I was in a similar postion to you, I had TNT Sports from BT (which I watched via Discovery+ app either on my MacBook or on Sky Q app) and then was offered HBO Max today.
What I did was to open the HBO Max app on Sky Q and then followed the instructions to login to the HBO Max app on my MacBook (I used my Discovery+ ID and password but nothing suggested this), got a numeric code which I entered into Sky Q app and TNT Sports was available to me.
But, none of the HBO series or movies were available, they all said "Get Access". Not sure whether this would have resolved itself in time, but to be sure I logged into My Sky app and activated HBO Max on the TV option page.
When I went back into Sky Q all series and most movies were then available (some movies still say "Get Access" but I imagine these are part of a paid upgrade which I do not want or need).
When I look at my Account page on HBO it shows I have TNT via BT and Basic with Ads from Sky.
Hope this helps.
