How to check the extension of a filename in a bash script?

Make

if [ "$file" == "*.txt" ]

like this:

if [[ $file == *.txt ]]

That is, double brackets and no quotes.

The right side of == is a shell pattern. If you need a regular expression, use =~ then.

I think you want to say "Are the last four characters of $file equal to .txt?" If so, you can use the following:

if [ ${file: -4} == ".txt" ]

Note that the space between file: and -4 is required, as the ':-' modifier means something different.

You just can't be sure on a Unix system, that a .txt file truly is a text file. Your best bet is to use "file". Maybe try using:

file -ib "$file"

Then you can use a list of MIME types to match against or parse the first part of the MIME where you get stuff like "text", "application", etc.