Soft launch and idea validation

Hi! I am(as probably a lot of people here) working with a remote team that spans across different time zones. Working remotely needs a lot of calls, and calls need to be scheduled. Usually, scheduling a call involves multiple round trips to some time zone conversion tool( i use WorldTimeBuddy for this), and the conversation usually goes like this:

-ok, let's do 3 pm my time.
-No, 3 pm your time is the late-night where I live, let's do 11 am.

I know about tools like Calendly, and such, but in my experience, some people might feel that it is rude if you just toss them your timeslot, without conversation and such. And, I often was in a situation where I scheduled a call via somebody's Calendly and the person just show up, because he didn't check it or something.

And I had an idea - what if I can make the process of manually scheduling the call, this conversation a little bit easier? For example, I can mark my availability on my timeline, and my counterparty can see this mark in his timeline, automatically converted to his time? And he can do the same, and we can see if there is an overlap?

I am learning to code, and this seemed like a good learning opportunity for me, so I decided to build a prototype. I've used it a bit with my friends, but I would like feedback. I feel that something might be missing, or there is a way to make it easier to understand, anyway, it lives here:

https://www.findmetime.app/

And, if there are bugs or something doesn't work, please tell me.