I've discussed the problem with Apple technical developer support. After a long discussion, they accepted that this is a bug on Apple side. It's escalated to the engineering team.

UPDATE: Apple Engineering team has provided the following information regarding this issue and it worked for me:

We were able to prevent the quitting behavior by adding NSSupportsAutomaticTermination = NO to info.plist

EDIT

This answer is not working, see the comments.

EDIT END

This is only possible, if you activate "Supports multiple windows":

My thoughts, why it is like this: macOS differentiates between applications and windows. So if your application can open only one window, closing that will tell macOS to close the application.

PS: I experienced some bugs in the "supports multiple windows" mode. I hope, that they will be removed soon.

Here is my solution, maybe someone is still looking for this :)

1st we need to have access to AppKit. In this link you can find a good explanation of how to do it, as well as some sneak peek on the next step. link

Once we have an AppKit bundle ready, and read the explanation of how to disable the zoom button on the window (on the link above), we are ready to do what we actually want; which is to avoid the app termination when the Close button is clicked. For that we will simply hijack the Close button and tell it to do what we need...

- (void) tweakWindowButtons
{
    NSArray *windows = NSApplication.sharedApplication.windows;
    
    NSWindowCollectionBehavior behavior = NSWindowCollectionBehaviorFullScreenAuxiliary | NSWindowCollectionBehaviorFullScreenNone;
    
    for (NSWindow *window in windows) {
        [window setCollectionBehavior:behavior];
        
        //-- Hijack close button action
        NSButton *button = [window standardWindowButton:NSWindowCloseButton];
        [button setTarget:self];
        [button setAction:@selector(closeButtonAction)];
        
        button = [window standardWindowButton:NSWindowZoomButton];
        [button setEnabled:NO];
    }
}

- (void) closeButtonAction
{
        NSApplicationActivationPolicy policy = NSApplicationActivationPolicyAccessory;
        
        //-- hide app icon and window
        NSApplication.sharedApplication.activationPolicy = policy;
    }
}

To bring the view back, set the policy to NSApplicationActivationPolicyRegular

BTW, I'm assuming we also have a statusbar icon that will be working as an anchor to the app.