#Dyalog APL, 19 17 16 bytes ≢+#⍎'\d'⎕R'&+',⊢

Takes string and returns

 ≢ length
+ plus
 # in root namespace
⍎ evaluation of
 '\d'⎕R'&+' regex append digits with a plus
, followed by
 ⊢ the unmodified string

–3 thanks to ngn

Dyalog APL, 19 17 16 bytes

≢+#⍎'\d'⎕R'&+',⊢ 

Takes string and returns

 ≢ length
+ plus
 # in root namespace
⍎ evaluation of
 '\d'⎕R'&+' regex append digits with a plus
, followed by
 ⊢ the unmodified string

–3 thanks to ngn

#Dyalog APL, 19 17 bytes ≢+(⍎'\d'⎕R'&+',⊢)

Takes string and returns

 ≢ length
+ plus
 ⍎ the evaluation of
    '\d'⎕R'&+' regex append digits with a plus
   , followed by
    ⊢ the unmodified string

–2 thanks to ngn

#Dyalog APL, 19 17 16 bytes ≢+#⍎'\d'⎕R'&+',⊢

Takes string and returns

 ≢ length
+ plus
 # in root namespace
⍎ evaluation of
   '\d'⎕R'&+' regex append digits with a plus
  , followed by
   ⊢ the unmodified string

–3 thanks to ngn

#Dyalog APL, 19 bytes ⍎+≢+#⍎¯1↓'\d'⎕R'&+'

Takes string and returns

 '\d'⎕R'&+' regex append digits with a plus
↓ drop
 ¯1 one trailing character
⍎ evaluate in
 # the root namespace
 + plus
 ≢ the length of the string
 + plus
  ⍎ the evaluation of the entire string
 

#Dyalog APL, 19 17 bytes ≢+(⍎'\d'⎕R'&+',⊢)

Takes string and returns

 ≢ length
+ plus
 ⍎ the evaluation of
     '\d'⎕R'&+' regex append digits with a plus
    , followed by
     ⊢ the unmodified string

–2 thanks to ngn