Count number of line in txt file when new line is inside data

Question

I have one txt file which has below data

Name    mobile  url message text
test11  1234567890  www.google.com  "Data Test New
Date:27/02/2020
Items: 1
Total: 3
Regards
ABC DATa
Ph:091 : 123456789"
test12  1234567891  www.google.com  "Data Test New one
Date:17/02/2020
Items: 26
Total: 5
Regards
user test
Ph:091 : 433333333"

Now you can see my last column data has new line character. so when I use below command

awk 'END{print NR}' file.txt

it is giving my length is 15 but actually line length is 3 . Please suggest command for the same

Edited Part: As per the answer given the below script is not working if there's no newline at the end of input file

awk -v RS='"[^"]*"' '{gsub(/\n/, " ", RT); ORS=RT} END{print NR "\n"}' test.txt 

Also my file may have 3-4 Million of records . So converting file to unix format will take time and that is not my preference. So Please suggest some optimum solution which should work in both case

head 5.csv | cat -A  
Above command is giving me the output

Name mobile url message text^M$

Answer 1

Using gnu-awk you can do this using a custom RS:

awk -v RS='"[^"]*"' '{gsub(/(\r?\n){2,}/, "\n"); n+=gsub(/\n/, "&")}
END {print n}' <(sed '$s/$//' file)

15001

Here:

• -v RS='"[^"]*"': Uses this regex as input record separator. Which matches a double quoted string
• n+=gsub(/\n/, "&"): Dummy replace \n with itself and counts \n in variable n
• END {print n}: Prints n in the end
• sed '$s/$//' file: For last line adds a newline (in case it is missing)

Code Demo