How to prevent JPG format from being saved as low 'quality'?

If the image has been saved with the appropriate Photoshop metadata, then the Save quality is known and will be used again when saving.

If the JPEG was created by another app or if this metadata has been removed, then using Save should bring up the JPEG Options dialog so that you can specify the required options. Subsequent saves will silently save without the JPEG Options dialog. If you Save As then the JPEG Options dialog will be presented with the known options prefilled.

You can setup Quick Export As JPEG, however, this will remove the embedded ICC profile and other metadata as it's intended for device/screen use.

So you are then left with creating an action and setting it with the "modal” control so that it's interactive:

Or you can use a script:

/*
Default JPEG Save to Baseline Standard.jsx
https://community.adobe.com/t5/photoshop-ecosystem-discussions/save-as-jpeg-again/td-p/12650865
Stephen Marsh, 12th January 2022 - v1.0
Info: Uses the standard Photoshop interface with preset JPEG options
*/

#target photoshop

if (app.documents.length > 0) {
    var docName = app.activeDocument.name.replace(/\.[^\.]+$/, '');
    try {
        // Use the previously saved path
        var docPath = app.activeDocument.path;
    } catch (e) {
        // If unsaved, prompt for save directory
        var docPath = Folder.selectDialog("Unsaved base file, select the output folder:");
    }
    saveJPEG(12);
} else {
    alert("You must have a document open!");
}

function saveJPEG(compValue) {
    // Using the standard Photoshop dialog windows
    var ID = function (s) {
        return app.stringIDToTypeID(s);
    };
    var AD = new ActionDescriptor();
    AD.putInteger(ID("extendedQuality"), compValue);
    AD.putEnumerated(ID("matteColor"), ID("matteColor"), ID("none"));
    AD.putObject(ID("as"), ID("JPEG"), AD);
    AD.putPath(ID("in"), new File(docPath + "/" + docName + ".jpg"));
    executeAction(ID("save"), AD, DialogModes.ALL);
}

1. Copy the code text to the clipboard
2. Open a new blank file in a plain-text editor (not in a word processor)
3. Paste the code in
4. Save as a plain text format file – .txt
5. Rename the saved file extension from .txt to .jsx
6. Install or browse to the .jsx file to run (see below)

https://prepression.blogspot.com/2017/11/downloading-and-installing-adobe-scripts.html

P.S.: If the JPEG image was put into a document and then saved as a PDF, then further lower level lossy compression in the PDF may have been used.