Barbarian: 4 attacks at level 5

[Zhorn]

Nah, this doesn’t work. There’s already a whole thread that’s several pages long on why, but you don’t get to attack and then drop your weapon and make another attack, especially if you already used your free object interaction that round.

You can make it work, but the order of things needs to be precise.
I'll dig down into all the relevant rules and rulings for those wanting a breakdown of it. This isn't meant as an @you, rlc, just covering what I can as I've seen a few times people make sweeping comments on 'this doesn't work' in piecemeal back and forth exchanges without referencing what rule they are getting their 'it doesn't work' from, often finding they have based it off a table ruling their DM has given them and not from RAW or dev clarification. I'll be as thorough as I can, but will be all ears if you know a reference I've missed.

To start with we need an understanding of dropping vs picking up or drawing a weapon.
Picking up or drawing a weapon will consume your object interaction, while dropping something out of hand does not.

https://twitter.com/JeremyECrawford/status/584435399767883776
The intent is that letting go of something requires no appreciable effort. But picking it up does.

Next is the restriction on what can be done during your Action and between Attacks. The general rule is you cannot interrupt an action to insert something in the middle of it unless there is specific timing mentioned in the rule. This is usually used to explain why you cannot insert a Bonus Action in the middle of an Action if it's trigger is the Attack Action, but you can if the trigger was an Attack (that's another conversation, just setting up for context, now back on track).
The rules for Object Interactions do make such mentions of timing

Other Activity on Your Turn
...
You can also interact with one object or feature of the environment for free, during either your move or your action. For example, you could open a door during your move as you stride toward a foe, or you could draw your weapon as part of the same action you use to attack.
...

Interacting with Objects Around You
Here are a few examples of the sorts of thing you can do in tandem with your movement and action:
draw or sheathe a sword
...
pick up a dropped axe
...


Breaking Up Your Move
...
Moving between Attacks
If you take an action that includes more than one weapon attack, you can break up your movement even further by moving between those attacks.
...

So Object Interactions can be done in tandem with Actions and Movement, and Movement is allowed to occur between attacks.
As an Object Interaction on your turn, you can draw a weapon (or two at once if using the Dual Wielder feat) or pick up a (singular) dropped weapon between Attacks, as either part of the next Attack being made, or as a function of your allowed Movement between Attacks.

Next up is the order of what types of Attacks are being made and whether they are under the Action or Bonus Action.

Once on each of your turns when you attack with a claw using the Attack action, you can make one additional claw attack as part of the same action.

The Attacks using the claws from Form of the Beast make no requirement of using different hands for each attack, and so you can do all your claw Attacks in the Attack Action with the same hand if you wish (important if your Barbarian is a shield wielder). For our purposes we only want to make two claw Attacks, one with out initial Attack from the Attack Action, an the second from the triggered feature that allows for one addition claw attack as part of the same action using the same claw (Important, as at this point our opposite hand is currently holding a weapon).
Before we use the Extra Attack, we have a couple more things to be aware of.
First up is our base allowance of attacking with different weapons during the Attack Action

https://media.wizards.com/2020/dnd/downloads/SA-Compendium.pdf
Q: When you use Extra Attack, do you have to use the same weapon for all the attacks?
A: Extra Attack imposes no limitation on what you use for the attacks. You can use regular weapons, improvised weapons, unarmed strikes, or a combination of these options for the attacks.

Then there's the condition we want to trigger. As we're intending to use a Bonus Action attack, we must satisfy the requirements.

Two-Weapon Fighting
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand.

So before we Attack with our weapon (having the light property assuming no Dual Wielder feat), we need to have one in each hand. As covered earlier we can draw or pick up as either part of Movement between Attacks, or as part of an Attack made with that weapon.
With a weapon now in each hand, we use the remaining Attack we have access to with Extra Attack, specifically using the most recently drawn/picked up weapon, and then follow it up with the Bonus Action allowed by meeting the conditions of Two-Weapon Fighting to Attack with the weapon we are holding in our opposite hand.

Now for sustainability each round, we need our starting and ending condition to always be the same.
Assuming no feats, start each round with a light melee weapon in each hand (also assuming you are already raging at this point with claws)

Step 1: Free actionless drop one weapon
Step 2: Attack Action with claw
Step 3: Free claw as part of the same action
Step 4: Object interaction pick up dropped weapon
Step 5: Extra Attack with that picked up weapon
Step 6: Bonus Action off hand attack with Two-Weapon Fighting

With our end state now matching our starting state.
4 Attacks with a level 5 Path of the Beast Barbarian, all 100% RAW compliant and supported without feats