I found a possible good way now for this after two years. Now it is possible to retrieve data through Graph API in the PowerApps. And it's super cool!
First, you can test the Graph API query below to fetch current user time zone in the Graph Explorer:
https://graph.microsoft.com/v1.0/me/mailboxSettings/timeZone
Example as below, Get method. The version can be v0.1 or beta. I tested both version works.
Before you run the query, please make sure to modify the permission under "Modify permissions" tab, consent to MailboxSettings.Read and MailboxSettings.ReadWrite permission.
After runing the query, you can find the value in the response is the Timezone name.

Second, you can create a blank PowerApps to test the Graph API.
In the app, add the "Office365Group" data connection.

Open moniter for the app, you will see the moniter does not have any log yet.


Back to the app editing page, insert a Button control and copy paste the below code to the "OnSelect" property of the button. Here
Set(varCurrrentUserTimezone,Office365Groups.HttpRequest("https://graph.microsoft.com/v1.0/me/mailboxSettings/timeZone","GET",""))

The varCurrrentUserTimezone is a UntypedObject that stored the response from the Graph API call.

Click on the button, then navigate to the moniter tab in the browser. You will see a HttpRequest Operation has been recorded. Click on Office365Group in Data source column -> click on Response. You will see the response body gives you the exact data that you get in Graph Explorer.

Just add a label below the button, with the below code, you will see the time zone name. We use ".value" here because it is where the time zone is stored.
varCurrrentUserTimezone.value

If you want, you can get the UTC time of the time zone by using the below code:
"(UTC"
& If(TimeZoneOffset() > 0, "-",TimeZoneOffset() < 0, "+","")
& Text(RoundDown(Abs(TimeZoneOffset()) / 60, 0),"00")
& ":"
& If(Mod(Abs(TimeZoneOffset()), 60) < 10, "0", "")
& Mod(Abs(TimeZoneOffset()), 60)
&")"

Myself has created a SharePoint list based on the window defualt time zone.
By useing the Lookup() for the Timezone list, I fetch the "Timezone desciprtion" (cities name).
LookUp(Timezone,Timezone=Label1.Text).'Timezone description'

I got inspired by Raze's cool video here Supercharge Your Power Apps with Direct Graph API Integration feel free to check this video.