A website/app shouldn't have to find your timezone. It should use whatever one you've set. If you've set your timezone to one you didn't want, I'm not sure what you'd expect other software is meant to do about that. Fix your config.
Even if the user set it in one time zone, if we store it without a proper offset (and preferably a locale), we cannot properly account for the user traveling to another place, daylight savings time, government time adjustments, leap time, etc. These complexities compound off each other and make proper scheduling and debugging time issues really, REALLY hard later on.
In the twenty years or so that I've been doing web dev, datetime is probably the single biggest gotcha I've seen developers (including myself) stumble into. Part of this is because the standard JS datetime handling is atrocious compared to any other language I've worked in. It doesn't really natively handle time zones well, and well carelessly cast them back and forth if you're not careful.
Moment and Luxon can help with this, lighter libs like date-fns can too with the right extensions, but out of the box JS is going to fuck it up. I promise. Another choice is to just use milliseconds to store everything, and convert that to the user's timezone only at the time of display. Every timestamp is stored as an epoch, and every user has their time zone (not just offset, because of daylight savings) recorded with their profile. Doing those two simple things can avoid most of the landmines.
And javascript natively converts epoch time to whatever timezone the client has set. If your user-agent (aka browser) is working on New York time, but you're in Tokyo, well, I'm not sure who else you have to blame but yourself if it shows you New York time when you didn't want that.
I had to fix so many of these in various databases and frontends, lol