No
Tentacle Slam is not technically an attack.
In the stat block, the other actions include the phrase Melee Weapon Attack while Tentacle Slam has no similar verbiage. Tentacle Slam does not call for making an attack roll with a d20.
Tentacle Slam is an action that causes grappled creatures to make saving throws. It does not qualify as an attack for the purposes of the Otyugh's Multiattack ability.
When an attack is not an attack
This prior answer explains what counts as an attack in the game mechanics. That answer draws upon the passage from the Player's Handbook:
If there's ever any question whether something you're doing counts as
an attack, the rule is simple: if you're making an attack roll, you're
making an attack (PH, p. 194)
There are many actions that would likely be considered "attacks" in-universe, but which are not attacks mechanically. Examples include grappling and spells with save versus damage effects.
When reading a term in the rules, interpret it with the definitions in the rules. When deciding how NPCs/monsters react to something, use common sense.
First, answering your text questions:
Yes, it can constrict the same target again.
Actually, I think this is the point. The block states
and the water weird can't constrict another target.
And nowhere it says it can't constrict the same target again. This is also confirmed by this answer.
It can also just change targets
Until this grapple ends, the target is restrained, the water weird tries to drown it, and the water weird can't constrict another target.
From the Grappling section on PHB:
The condition specifies the things that end it, and you can release the target whenever you like (no action required).
So, the Water Weird can just release the current target, ending the grapple, and then constrict another target.
So, essentially
it stops being a threat as long as it's grappling a character?
This part of your question is off. That is not how Water Weird/Constrict is supposed to work.
About your title question
Your setup is kinda suboptimal for the Water Weird
As I read his stat block, he is supposed to be fighting under water. In particular, this feature
Invisible in Water. The water weird is invisible while fully immersed in water.
is completely lost in your setup. This should decrease the challenge of the party considerably.
So, I would say
Yes, in your setup, it might be too weak for three 3rd level PCs
But not for the reason you thought, but because it loses a major feature - permanent invisibility.
As a Side note on resistances and immunities
You didn't mention your PCs' classes nor their items. So, I would like to add a caveat to my answer.
Damage Resistances: fire; bludgeoning, piercing, and slashing from nonmagical attacks
Damage Immunities: poison
So, if your party is too martial-based (e.g. a Fighter and a Rogue) and these martial PCs don't have magical weapons yet (which is likely by 3rd level), the resistance to physical damage can make the fight harder again, changing my answer.
As a final note
A CR3 monster has 700 XP on it. Against your party, it means a barely Hard (675 XP threshold) encounter. It's far away from a Deadly encounter (1200 XP threshold). So any CR3 monster shouldn't be that hard, even by book's definition - hard encounters mean there is a slim chance that a PC dies.
These XP thresholds can be calculated using Basic Rules or DMG section on Creating Encounters.
Best Answer
By the RAW, no, but it's a DM call
There is nothing specific in the rules about readying an action to strike a creature with reach when it comes in to attack with a body part, and the rule is that you can only make melee attacks against creatures that are within your reach. Despite the attacker having a long reach, its body is way over there, so by default, you can't do this. However, a DM could certainly to decide to allow it based on the situation at hand.
It's reasonable to say that you can chop at a limb as it comes towards you; but it's equally reasonable to say that a dragon's claw is too heavily scaled and moving too fast during an attack to present a target for a melee attack.
Now, if you're being grappled by an Enormous Tentacle, it's pretty hard to argue against being able to attack it, since it's literally wrapped around your body; but again, this is down to the DM and the exact scenario at the table. There's no official rule that says this is possible, but that's why we have human DMs at the table.