UserInfo.getTimeZone() can be used to get the current User time zone in an Apex class.

Use the following code for your reference.

Sample Code:

TimeZone tz = UserInfo.getTimeZone();
System.debug( 
    tz 
);

So, UserInfo.getTimeZone() can be utilized to get the current user time zone in Salesforce Apex. Check the following for Business Hours check.

Check date time occurs within Business Hours Salesforce Apex