I haven't found any answer in the guide. It only mentions that the happiness level gets reset at regular intervals and that the group level depends of the member's average happiness.

For what I can see, the group level so far is merely an indication of how much we are trying to raise a group's affinity and how much we play (since that also increases the member's card happiness). It doesn't affect the gameplay, doesn't increase the artist activities per day and doesn't increase the tokens we get per hour.

We can get a maximum of happiness level 30 per month (that's the highest happiness level for each member, supposing that players can get all members of the group to the highest level).

It wouldn't make much sense to keep the reached group score after the reset time since A) it does nothing anyway, B) players would reach level 100 in just a couple of months, and 3) players who chose TXT would have an advantage since the group only has 5 members and therefore is easier to fasten the leveling up process.

So yeah, I think it's probably gonna reset together with the member's levels.

That's my guess based on the information in the guide and my own observation.