The target does not need to be under the grappled condition in order to shoved. I'm under the impression that 'shove' is an independent action from grapple. Note: The DC to escape these special attacks is in the stat block, not derived from skills and proficiency and so can't be boosted as a Druid levels. That said, if the target makes the DC 16 check they can just move into melee. The main benefit here is IF the enemy stays Grappled the Giant Octopus can attack them and unless they have 15' reach they can't attack the Giant Octopus. This is also true if the Moon Druid turns into a Giant Octopus and uses Tentacles from up to 15' away. Note: the Giant Toad can swallow 1 target and still bite another, but can only have 1 swallowed. The Giant Toad loses nothing in attempting this as it is probably going to bite anyways. The escape attempt is easy, but uses up an Action. This is nice because the enemy is Restrained so give Adv and has DisAdv. That said if that 4th lvl Moon Druid (because they have swim speeds) turns into a Giant Toad (CR:1) and bites an enemy they are automatically grappled and restrained. It's going to be rare that anything is better than Bite & Claw. Or the Moon Druid can use MultiAttack to attack 4 times over 2 turns for Bite and Claw. then all melee attacks will have Adv on the target and the target will have DisAdv to attack anyone else or will need to win a Grapple check to escape. She can spend 2 Actions over 2 turns attempting to Grapple an enemy and Shove them to the ground. Her Athletics is now +6 (+4 Strength for Brown Bear and +2 Proficiency). Image a lvl 4 Moon Druid is trained in Athletics and turns into a Brown Bear.
It's probably going to be more effective just to attack and deal damage unless there are specific circumstances.
The only positive is it makes it hard for them to run away, because half their movement is spend standing and they can't Disengage so you get AoOs. Ie: if they beat a single grapple, they escape and can stand up. That requires you to succeed on 2 Athletics checks and they only need to succeed on 1 to negate both. The best thing about it is that if you also Shove the enemy they will be Prone. It's extremely good in a small number of circumstances, but not something to build a character around.Ī basic grapple reduces their speed to 0. This is personal opinion but Grappling isn't very good in 5e.