A more intuitive version of a JS date formatter. This function leverages Intl.DateTimeFormat().

formatIntlDate.js

var formatIntlDate = (() => {
  const codeToOpts = [...'Y=year M=month D=day H=hour h=hour m=minute s=second S:1 SS:2 SSS:3 MMM=month:short MMMM=month:long DDD=weekday:short DDDD=weekday:long A=hour:2D a=hour:2D Z:Offset ZZ:Offset ZZZ:Generic ZZZZ: J=year:numeric,month:2D,day:2D,hourCycle:h23,hour:2D,minute:2D,second:2D,fractionalSecondDigits:3,timeZoneName:longOffset'.replace(/(\w)=\w+(?= |$)/g, '$&:numeric $1$&:2D').replace(/hour/g, 'hourCycle:h23,$&').replace(/Z:/g, 'Z=timeZoneName:long').replace(/S:/g, 'S=fractionalSecondDigits:').replace(/2D/g, '2-digit').matchAll(/(\w+)=(\S+)/g)]
    .reduce(
      (codeToOpts, [_, code, strOpts]) => {
        codeToOpts[code] = [...strOpts.matchAll(/(\w+):([^,]+)/g)].reduce(
          (opts, [_, key, value]) => {
            opts[key] = value;
            return opts;
          },
          {}
        );
        return codeToOpts;
      },
      {}
    );

  /**
   * Formats a date as a string.
   * @param {Date} date
   *   The valid date object to format.
   * @param {string} format
   *   The format to use.  You can use any of the following metacharacters:
   *     Y, YY, M, MM, MMM, MMMM, D, DD, DDD, DDDD, H, HH, h, hh, m, mm, s, ss,
   *     S, SS, SSS, Z , ZZ, ZZZ, ZZZZ, d, dd, ddd, dddd, t, tt, ttt, tttt, A,
   *     a, J
   * 
   *   Wrap substrings in single quotes or double quotes to avoid formatting the
   *   metacharacters.  To escape a quote character prefix it with a backslash.
   * @param {?FormatIntlDateOptions=} options
   *   Optional.  Allows you to specify the locale and/or the timezone to use
   *   when producing the formatted date/time string.
   * @returns {string}
   *   A string which represents the given date object.
   */
  function formatIntlDate(date, format, options) {
    const {locale, timeZone} = Object(options);
    return format.replace(
      /("|')((?:(?:(?!\1)[^\\])+|\\["'])*)\1|(?=(.))(?:[AJa]|[YHhms]{1,2}|[DMZdt]{1,4}|S{1,3})/g,
      (pattern, strDelim, strInnards, pattern0) => {
        if (strDelim) return strInnards.replace(/\\(.)/g, '$1');
        if (pattern0 === 'd' || pattern0 === 't') {
          return new Intl.DateTimeFormat(locale, {
            [pattern0 === 'd' ? 'dateStyle' : 'timeStyle']: ['short', 'medium', 'long', 'full'][pattern.length-1],
            timeZone
          }).format(date);
        }
        const opts = codeToOpts[pattern];
        const dtf = new Intl.DateTimeFormat((pattern === 'J' || pattern === 'Z') ? 'en-US' : locale, {...opts, timeZone});
        if (pattern === 'J') {
          return (dtf.format(date) + 'Z')
            .replace(/^(..).(..).(....), ([\d:.]+) (?:GMT([-+\d:]+)Z|GMT(Z))$/, '$3-$1-$2T$4$5$6');
        }
        let {type, value} = dtf.formatToParts(date).find(({type}) => type === 'fractionalSecond' || opts[type]);
        if (pattern === 'Z') return value === 'GMT' ? '+00:00' : value.slice(3);
        if (pattern === 'a') return +value < 12 ? 'am' : 'pm';
        if (pattern === 'A') return +value < 12 ? 'AM' : 'PM';
        if (pattern === 'h' || pattern === 'hh') value = value % 12 || 12;
        const optsTypeValue = opts[type];
        return (optsTypeValue === 'numeric' && /^0./.test(value))
          ? +value
          : (optsTypeValue === '2-digit' && /^.$/.test(value))
            ? '0' + value
            : value;
      }
    );
  }

  return formatIntlDate;

  /**
   * @typedef FormatIntlDateOptions
   * @property {string=} locale
   *   The locale to use for names in the formatted date (eg. "en", "pt-BR").
   * @property {string=} timeZone
   *   The timezone to use for displaying the date/time as a string (eg.
   *   "America/Los_Angeles").
   */
})();

~example_run-all_metacharacters.js

const format = `
  "YY":\tYY
  "Y":\tY
  "MMMM":\tMMMM
  "MMM":\tMMM
  "MM":\tMM
  "M":\tM
  "DDDD":\tDDDD
  "DDD":\tDDD
  "DD":\tDD
  "D":\tD
  "HH":\tHH
  "H":\tH
  "hh":\thh
  "h":\th
  "mm":\tmm
  "m":\tm
  "ss":\tss
  "s":\ts
  "SSS":\tSSS
  "SS":\tSS
  "S":\tS
  "A":\tA
  "a":\ta
  "ZZZZ":\tZZZZ
  "ZZZ":\tZZZ
  "ZZ":\tZZ
  "Z":\tZ
  "dddd":\tdddd
  "ddd":\tddd
  "dd":\tdd
  "d":\td
  "tttt":\ttttt
  "ttt":\tttt
  "tt":\ttt
  "t":\tt
  "J":\tJ
`;

for (const timeZone of ['Australia/Adelaide', 'UTC', 'America/New_York', 'America/La_Paz']) {
  console.group(`Timezone = ${timeZone}`);
  for (const locale of ['en', 'es', 'pt', 'ja', 'ar']) {
    console.log(`locale = ${locale}` + formatIntlDate(new Date('2001-02-03 16:05:06.007'), format, {locale, timeZone}));
  }
  console.groupEnd();
}

~example_run-generic.js

const format = 'DDDD, D MMMM, Y @ h:mm:ss.SSS (ZZZZ)';

for (const timeZone of ['Australia/Adelaide', 'UTC', 'America/New_York', 'America/La_Paz']) {
  console.group(`Timezone = ${timeZone}`);
  for (const locale of ['en', 'es', 'pt', 'ja', 'ar']) {
    console.log(`locale = ${locale}:  ` + formatIntlDate(new Date(), format, {locale, timeZone}));
  }
  console.groupEnd();
}