Is ruling different for NFHS and NCAA-OBR?
 

20. B9 hits a grounder to F6. F6’s
throw to F3 bounces and ends up
trapped against F3’s body by his arm.
F3, who is standing on first base, holds
the ball securely in that manner while
B9 touches first base. After B9 has
crossed the bag, F3 pulls the ball out
and shows it to the umpire. F3 never
juggled or bobbled the ball.
a. B9 is out.
b. B9 is safe.

Safe in all codes. See the definition of tag.

What about this?
 

NFHS 2-24-1 ART. 1 . . . A force-out is a putout during which a runner who is being forced to advance is tagged out, or is put out by a fielder who holds the ball while touching the base toward which the forced runner is advancing (9-1-1 for special case.)

F3 is holding the ball, just not in his hand or glove.

It needs to be held in the hand or glove.

See 2-Catch for some description of this, and there's a specific case on it as well (under 2.Catch)

The situation you describe is not yet control. Safe in all baseball (and all softball) codes.