How to show event dates with local time

Hi Hester,
Most likely you're mixing strings with dates, which won't compute nicely. Date objects are pretty strict, it's usually best to approach conversions by adding/subtracting a separate date object and then converting to a string:
const [timeZone] = new Date().toString().match(/([A-Z]+[+-][0-9]+)/);
var offset = new Date().getTimezoneOffset();
const date = new Date('August 29, 2022 16:00:00'); //our date to be converted


var offsetDate = new Date(date*1 + offset*60*1000)  //creating a new date by converting our original date and offset to miliseconds and adding them together
var offsetDateText = offsetDate.toLocaleDateString() + " " + timeZone //a string of the new date

console.log(offsetDateText) // "8/29/2022 GMT+1000"
Tinker with options as need be.
Good luck!

bgooldfed thank you so much! The formula to convert to a local date was especially where I felt utterly lost.

Below are some changes I made for posterity and in case it's beneficial for others.
const [timeZone] = new Date().toString().match(/([A-Z]+[+-][0-9]+)/);
var offset = new Date().getTimezoneOffset();
const date1 = new Date('August 29, 2022 14:00:00'); //our date to be converted
const options = { weekday: 'short', year: '2-digit', month: 'short', day: 'numeric' }; // some additional formatting to show weekday more clearly

console.log(timeZone) // GMT+1000 Logged and embedded timeZone seperately, also because it gave me more control over formatting in the survey
Qualtrics.SurveyEngine.setEmbeddedData('timeZone', timeZone);

var offsetDate1 = new Date(date1*1 - offset60*1000)
// creating a new date by converting our original date
// and offset to miliseconds and adding them together
//Adjusted the calculation to state - offset*60*1000 instead of + offset*60*1000 I think it's because offset returned is negative when +GMT and positive when -GMT. This seems to work 🤷‍♀
var offsetTimeText1 = offsetDate1.toLocaleTimeString([], {hour:'2-digit', minute: '2-digit'}) /*+ " " + timeZone //a string of the new date*/

// Added toLocaleTimeString so that I could have more control over formatting for date and time. Also commented out timezone as I'm embedding and adding a field separately for formatting

// Added undefined locale and date formatting options
var offsetDateText1 = offsetDate1.toLocaleDateString(undefined, options); //a string of the new date

console.log(offsetTimeText1)  // "14:00:00"
console.log(offsetDateText1)  // "Mon, 29 Aug 22"

Qualtrics.SurveyEngine.setEmbeddedData('offsetTimeText1', offsetTimeText1);
Qualtrics.SurveyEngine.setEmbeddedData('offsetDateText1', offsetDateText1);

For anybody else visiting this thread struggling with dates, bear in mind that they are just a number expressed in miliseconds. So if all else fails, working in miliseconds should be reliable.