More interesting answer using the Canvas builtin (27 bytes):
^{20 bytes if trailing whitespaces were allowed: try it online.}

€g€D ̈2.ýIðIδ∍.ιJŽDāS.Λ¶¡ðδÜ

Input as a list of words; output as a list of lines.

Try it online.

€g # Get the length of each word of the (implicit) input-list
 €D # Create a copy of each length in the list, keeping a flattened list
   ̈  # Remove the trailing item
 2.ý # Intersperse it with 2 as delimiter
I # Push the input-list of words again
 ð  # Push a space character: " "
 I # Push the input-list yet again
 δ # Map over each word in the input-list with the " " as argument:
 ∍ # Extend the space to a length equal to the word
 .ι # Interleave this list of spaces with the list of words
 J # Join it to a single string
ŽDā # Push compressed integer 3474
 S # Convert it to a list of digits
.Λ # Use the modifiable Canvas builtin with these three arguments
 ¶¡ # Split it on newlines
 δ # Map over each inner line:
 ð Ü # Trim trailing spaces
 # (after which the list of lines is output implicitly)

See this 05AB1E tip of mine (section How to compress large integers?) to understand why ŽDā is 3474.

Additional information about the Canvas builtin Λ/.Λ:

€g€D ̈2.ýIðIδ∍.ιJŽDāS creates the following Canvas arguments:

• Lengths (€g€D ̈2.ý): e.g. [11,2,11,2,7,2,7,2,3,2,3,2,4,2,4,2,4] for input ["programming","puzzles","and","code","golf"]
• Characters (IðIδ∍.ιJ): e.g. "programming puzzles and code golf " for input ["programming","puzzles","and","code","golf"]
• Directions (ŽDāS): [3,4,7,4], which translates to \$[↘,↓,↖,↓]\$

Step 2: Draw 2-1 characters (" ") in direction 4 (\$↓\$):

p
 r
 o
 g
 r
 a
 m
 m
 i
 n
 g

Step 3: Draw 11-1 characters (" ") in direction 7 (\$↖\$):

p
 r
 o
 g
 r
 a
 m
 m
 i
 n
 g
 

Step 4: Draw 2-1 characters ("p") in direction 4 (\$↓\$):

p
 r
p o
 g
 r
 a
 m
 m
 i
 n
 g

Step 5: Draw 7-1 characters ("uzzles") in direction 3 (\$↘\$):

p
 r
p o
 u g
 z r
 z a
 l m
 e m
 s i
 n
 g

IðIδ∍.ιJ could alternatively be εðy∍«}J or íD€gúíJ, but I've been unable to find anything shorter.

More interesting answer using the Canvas builtin ((削除) 27 (削除ここまで) 25 bytes):
^{(削除) 20 (削除ここまで) 19 bytes if trailing whitespaces were allowed: try it online.}

€gDø4.ý ̃I€ûðoý374S.Λ¶¡ðδÜ

-2 bytes thanks to @emanresuA.

Input as a list of words; output as a list of lines.

Try it online.

€gDø4.ý ̃I€ûðoý374S.Λ¶¡ðδÜ
€g # Get the length of each word of the (implicit) input-list
 Dø # Convert each value to a pair of this value with a Duplicate + Zip/transpose
 4.ý # Intersperse this list of pairs with 4 as delimiter
  ̃ # Flatten it to a single list
I # Push the input-list of words again
 €û # Palindromize each word
 ðoý # Join this list with " " (2 spaces) delimiter
ŽDā # Push 374
 S # Convert it to a list of digits: [3,7,4]
.Λ # Use the modifiable Canvas builtin with these three arguments
 ¶¡ # Split it on newlines
 δ # Map over each inner line:
 ð Ü # Trim trailing spaces
 # (after which the list of lines is output implicitly)

Additional information about the Canvas builtin Λ/.Λ:

€gDø4.ý ̃I€ûðoý374S creates the following Canvas arguments:

• Lengths (€gDø4.ý ̃): e.g. [11,11,4,7,7,4,3,3,4,4,4,4,4,4] for input ["programming","puzzles","and","code","golf"]
• Characters (I€ûðoý): e.g. "programmingnimmargorp puzzleselzzup andna codedoc golflog" for input ["programming","puzzles","and","code","golf"]
• Directions (374S): [3,7,4], which translates to \$[↘,↖,↓]\$

Step 2: Draw 11-1 characters ("nimmargorp") in direction 7 (\$↖\$):

p
 r
 o
 g
 r
 a
 m
 m
 i
 n
 g

Step 3: Draw 4-1 characters (" p") in direction 4 (\$↓\$):

p
 r
p o
 g
 r
 a
 m
 m
 i
 n
 g

Step 4: Draw 7-1 characters ("uzzles") in direction 3 (\$↘\$):

p
 r
p o
 u g
 z r
 z a
 l m
 e m
 s i
 n
 g

€gDø4.ý ̃ could alternatively be εgD4)} ̃ ̈ or €gDø4ドル¦ ̃, but I've been unable to find anything shorter.