A troubling doubling

Question

The answers to all the clues below are rhyming doublets.

(Except there is one rhyming triplet, which is marked.)

So if I say:

Hirsuite stone fruit

you reply:

Hairy cherry

Or if I say:

Friendly—but not romantic—proctological exam

you reply:

Platonic colonic

There are four sets of these clues below. Your goals are to:

1. Figure out each rhyming couplet.
2. Discover the hidden word(s) in each set of answers.
3. Explain how the 4 hidden word(s) are related to one another.

Note: The rhymes are generally decent, but perhaps not unimpeachable. I tried.

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Set 1

1. Didn’t really make a difference

2. Hanging someone, most commonly

3. Motionless pharmaceutical

4. Enter verification code for new version of software

5. Beakers, flasks, pipettor, balance, Bunsen burner, safety goggles, etc.

6. What a lidocaine injection often does

Set 2

1. Obese rodent

2. Taste failure

3. Begin separated

4. Approach equipment

5. Leave before the FBI kicks in the door

Set 3

1. Prepared a citrus beverage

2. It is used to draw the Penguins' or Sharks' logos on the ice

3. One who will never be promoted to general

4. A peppy withdrawal from battle

5. Exemplary unagi

Set 4

1. Cheerful Twist

2. The yellow fruits belonging to the grandmother of Derek Jeter’s fiancée (triplet)

3. A breathtaking building destruction

4. It’s not present in a theater after an emotional performance

5. Google Images SafeSearch does this

Answer 1

Set 1

Didn’t really make a difference

Lacked Impact

Hanging someone, most commonly

Noose Use

Motionless pharmaceutical

Still Pill

Enter verification code for new version of software

Authenticate Update

Beakers, flasks, pipettor, balance, Bunsen burner, safety goggles, etc.

Laboratory Inventory

What a lidocaine injection often does

Numbs Gums

Set 2

Obese rodent

Fat Rat

Taste failure

Eat Defeat

Begin separated

Start Apart

Approach equipment

Near Gear

Leave before the FBI kicks in the door

Evade Raid

Set 3

Prepared a citrus beverage

Made (Lemon)Ade

It is used to draw the Penguins' or Sharks' logos on the ice

Rink Ink

One who will never be promoted to general

Eternal Colonel

A peppy withdrawal from battle

Upbeat Retreat

Exemplary unagi

Ideal Eel

Set 4

Cheerful Twist

Jolly Oli

The yellow fruits belonging to the grandmother of Derek Jeter’s fiancée (triplet)

Hannah's Nanna's Bananas

A breathtaking building destruction

Amazing Razing

It’s not present in a theater after an emotional performance

Dry Eye

Google Images SafeSearch does this

Excludes Nudes

What links each set is:

The initial letters of each answer, so we get
Set 1:LINUS PAULING
Set 2:FRED SANGER
Set 3:MARIE CURIE
Set 4:JOHN BARDEEN

And they are all:

People who have won Nobel Prizes Twice

With thanks to Deusovi, Lighthart, whrrgarbl and especially Wesley Situ