Dual x86_64/arm64 Java application running under x86_64 emulation on a M1 machine

How comes that the same application runs under emulation or not depending on whether it is started from the command line or from the Finder?

There can be all sorts of reasons for that. However, my initial port of call would be this:

That is, the executable file within the application is a shell script

Using a shell script for your main executable is an ongoing source of problems [1] and something I specifically recommend against. If you must do this trampoline thing, switch to a native trampoline. I recently helped a developer with a different issue caused by the same problem and, as part of that, I created a simple trampoline in 39 lines of C (see below).

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—
Quinn “The Eskimo!” @ Developer Technical Support @ Apple
let myEmail = "eskimo" + "1" + "@" + "apple.com"

[1] For example, the TCC issue described in in On File System Permissions.

#include <libgen.h>
#include <mach-o/dyld.h>
#include <stdio.h>
#include <stdlib.h>
#include <sys/param.h>
#include <unistd.h>

extern char **environ;

static void fail(const char * message) {
    fprintf(stderr, "%s\n", message);
    exit(EXIT_FAILURE);
}

int main(int argc, char **argv) {
    #pragma unused(argc)
    #pragma unused(argv)

    char execPath[MAXPATHLEN];
    uint32_t execPathSize = sizeof(execPath);
    
    int success = _NSGetExecutablePath(execPath, &execPathSize) >= 0;
    if ( ! success ) { fail("_NSGetExecutablePath failed"); }
    
    const char * dirPath = dirname(execPath);
    if (dirPath == NULL) { fail("dirname failed"); }
    
    char * newPath;
    success = asprintf(&newPath, "%s/../MacOS/RealExecutable", dirPath) >= 0;
    if ( ! success ) { fail("asprintf failed"); }

    char * resourcePath;
    success = asprintf(&resourcePath, "%s/../Resources/Greeting.txt", dirPath) >= 0;
    if ( ! success ) { fail("asprintf failed"); }

    char * arguments[3] = { newPath, resourcePath, NULL };
    (void) execve(newPath, arguments, environ);
    fail("execve failed");
}