When veneering a panel, does the balancing veneer grain direction need to match the face veneer grain direction. My intuition would say yes, but then I look at the circular tables with a radial pattern and presume that the balancing veneer does not match. Appreciate any input.
Thanks.

Purists will insist that grain direction must be the same. It makes sense you would think. In my experience it is less of a factor than applying a backer of any species or direction.
I have no science or specific experimentation to back this up other than twenty years of layups but I feel that just the applying veneer with the same glue is enough to balance a panel (within reason).
Veneer being very thin imparts very small forces to a panel. The force will not be enough to distort a normal glue up.
Applying a moisture laden adhesive to one side and locking it into the expanded dimension will distort a panel. It will also over time impede moisture gain and loss one a single side. I feel the cured adhesive has more of an impact on moisture gain and loss than the veneer.
When working with thick veneers then pure balancing rules apply.
Just my opinion and I am sure you will get others.

Depends on the core thickness, and the wood specie and m/c.
We do a lot of table tops with 1" and 1-1/8" PBC and have few issues.
Using 11/16 core it's more critical. We mostly use same veneer for back or at least similar density. It also helps to use lower heat settings when pressing and keep panels flat & weighted until cool (and after also)

As a general rule, yes. Ideally same thickness, same species. Good luck with the project. Can't wait to see how it turns out.