Why doesn’t `git diff` invoke external diff tool?

I get the in-terminal diff display. I this should not happen, because I have set up an external diff tool

Yes, it should: diff.external is for “in-terminal diff display”.

(from git config man page)

diff.external

If this config variable is set, diff generation is not performed using the internal diff machinery, but using the given command.
Can be overridden with the GIT_EXTERNAL_DIFF environment variable.
The command is called with parameters as described under “git Diffs” in git(1). Note: if you want to use an external diff program only on a subset of your files, you might want to use gitattributes(5) instead.

The question you link explains why meld wouldn’t be able to play the role of an “external diff”.

Viewing a diff visually with another tool is done with:

git difftool --dir-diff shaOfHisCheckIn^!
git difftool --tool=meld --dir-diff shaOfHisCheckIn^!
git difftool -t meld -d shaOfHisCheckIn^!

meld can be configured on Windows as a difftool: see “Git Diff and Meld on Windows”.

If you wanted to configure meld for git diff, you could (on Ubuntu) use the diff.external, but with a wrapper script:

create a file called git-diff.sh, using the following content:

#!/bin/bash
meld "$2" "$5" > /dev/null 2>&1

Save this to a location such as /usr/local/bin, giving it executable rights:

$ sudo mv git-diff.sh /usr/local/bin/
$ sudo chmod +x /usr/local/bin/git-diff.sh

The final step is to open your $HOME/.gitconfig file and add the following few lines:

[diff]
        external = /usr/local/bin/git-diff.sh

The next time you type git diff in a Git project with changes, Meld will be launched showing you a split-pane diff viewer.
Note that you are required to close the open instance of meld before the next diff viewer is opened.

will notes in the comments:

That wrapper script works great on my Ubuntu system.

I did discover a gottcha: I detached the meld command as so:

meld "$2" "$5" > /dev/null 2>&1 &

Kept failing to open the $2 file (tempory file).
What happens? Well, git removes $2 once the wrapper exits.
My suggestion, if you wish to detach copy the tmp file, invoke meld and remove tmp file yourself.

will proposes the gist gist-meld.bash, using meld --newtab, as seen here:

#!/bin/bash
#  * expects meld to be on your default PATH
#
function detach_meld()
{
    local f1="/tmp/mld1-$(basename "$1")"
    local f2="/tmp/mld2-$(basename "$2")"
    
##  echo "f1 = ${f1}"
##  echo "f2 = ${f2}"

    cp "$1" "${f1}"
    cp "$2" "${f2}"
#
    (meld  --newtab  "${f1}" "${f2}" ; rm  "${f1}"  "${f2}" ) > /dev/null 2>&1  &    
}

detach_meld  "$2"  "$5"