Why does regex `“\.pdf”` match `/…/pdf…/…` in gawk, but not in mawk

1. In POSIX awk,
   Is there a builtin function which can achieve either of the two objectives?

No. You can achieve the same effect, but not with a single builtin function.

Does the match builtin function only find the leftmost and longest match?

Yes. Regular expressions in POSIX awk (and GNU awk) are always greedy (i.e. longest match always wins).

To achieve the first objective, is it a correct way to repeatedly apply match to the suffix of the target string created by finding each match and removing the match and the prefix before it from the target string?

Yes, but if you want 100% compatibility with gsub() the details are pretty tricky.

Is https://gist.github.com/mllamazing/a40946fcf8211a503bed a correct implementation?

Mostly, if you remove the gsub line. The devil is in the details: the code will loop if regex is an empty string. Classic awk didn't allow empty regexps, but IIRC nawk did. To fix that you could do something like this:

function FindAllMatches(str, regex, match_arr) {

    ftotal = 0;
    ini = RSTART;
    leng = RLENGTH;

    delete match_arr;

    while (str != "" && match(str, regex) > 0) {
        match_arr[++ftotal] = substr(str, RSTART, RLENGTH)
        str = substr(str, RSTART + (RLENGTH ? RLENGTH : 1))
    }

    RSTART = ini;
    RLENGTH = leng;
}

That's not 100% compatible to gsub() however, because

$ echo 123 | awk '{ gsub("", "-") } 1'
-1-2-3-

while the function above finds only 3 matches (namely, it misses the match at the end).

You could try this instead:

function FindAllMatches(str, regex, match_arr) {

    ftotal = 0;
    ini = RSTART;
    leng = RLENGTH;

    delete match_arr;

    while (match(str, regex) > 0) {
        match_arr[++ftotal] = substr(str, RSTART, RLENGTH)
        if (str == "") break
        str = substr(str, RSTART + (RLENGTH ? RLENGTH : 1))
    }

    RSTART = ini;
    RLENGTH = leng;
}

This fixes the problem above, but it breaks other cases: if str = "123" and regex = "[1-9]*" the function finds two occurrences, 123 and the empty string at the end, while gsub() finds only one, 123.

There may be other similar differences, that I can't be bothered to hunt right now.

2. In Gawk,

   does array after a call patsplit(string, array, fieldpat, seps) store the matches as required in the second objective?

Mostly yes. However, corner cases related to regexps can be unexpectedly subtle. There may be some differences, as above.

Can the locations of the match location be found from array and seps, based on that seps[i] is the separator string between array[i] and array[i+1]?

Yes.

It's a bit hacky, but since you are already using a perl compatible RE, you could use \K "keep left" modifier to match everything in your expression (and anything else up to the next line end) but exclude it from the output:

pdfgrep -Pn '(?s)image\s+?not\s+?available.*?$\K'  main_text.pdf

The output will still include the : separator however.