Create a new Apex class and define the necessary instance variables and methods to handle the data manipulation and the Strava API integration.
Define a method that will retrieve the necessary event and registration data. You can use SOQL queries to retrieve the event and registration data related to the Contact record.
Define a method that will make a callout to the Strava API using the Strava member ID and club ID. You can use the Http class in Apex to make the callout.
Parse the response from the Strava API to extract the necessary data, such as the Strava activity data.
Define a method that will update or create a new Strava Activity record associated with the Event Registration. You can use the Database class in Apex to perform the DML operation.
Add error handling and logging to ensure that any errors or issues are properly handled and logged for debugging purposes.
Finally, create a Lightning component that will allow the user to execute the Apex class manually on the Event page. You can use the lightning:button component to trigger the execution of the Apex class.
Here's some sample code to get you started:

public with sharing class StravaSync {
    public static void syncStravaData(Set<Id> registrationIds) {
        
        // First, query for all the registrations with the given Ids
        List<EventApi__EventRegistration__c> registrations = [
            SELECT Id, Contact__r.Strava_Member_Id__c, Event__r.Start_Date__c, Event__r.End_Date__c
            FROM EventApi__EventRegistration__c
            WHERE Id IN :registrationIds AND EventApi__Status__c = 'Active'
        ];
        
        // Then, for each registration, make a callout to the Strava API and fetch the member data
        for (EventApi__EventRegistration__c registration : registrations) {
            
            // Check if the Contact has a Strava Member Id
            if (String.isNotBlank(registration.Contact__r.Strava_Member_Id__c)) {
                
                // Make the callout to the Strava API
                String stravaMemberId = registration.Contact__r.Strava_Member_Id__c;
                String startDate = registration.Event__r.Start_Date__c.formatGMT('yyyy-MM-dd');
                String endDate = registration.Event__r.End_Date__c.formatGMT('yyyy-MM-dd');
                String stravaUrl = 'https://www.strava.com/api/v3/athlete/activities?after=' + startDate + '&before=' + endDate;
                HttpRequest req = new HttpRequest();
                req.setEndpoint(stravaUrl);
                req.setMethod('GET');
                req.setHeader('Authorization', 'Bearer ' + getStravaAccessToken());
                Http http = new Http();
                HttpResponse res = http.send(req);
                
                // Parse the JSON response and create/update Strava Activity records as necessary
                List<StravaActivity> activities = (List<StravaActivity>) JSON.deserialize(res.getBody(), List<StravaActivity>.class);
                List<EventApi__StravaActivity__c> stravaActivities = new List<EventApi__StravaActivity__c>();
                for (StravaActivity activity : activities) {
                    if (activity.athlete.id == stravaMemberId) {
                        EventApi__StravaActivity__c stravaActivity = new EventApi__StravaActivity__c();
                        stravaActivity.Name = activity.name;
                        stravaActivity.Start_Date_Time__c = DateTime.parse(activity.start_date).addHours(7); // Adjust for time zone
                        stravaActivity.Distance__c = activity.distance;
                        stravaActivity.Max_Speed__c = activity.max_speed;
                        stravaActivity.Average_Speed__c = activity.average_speed;
                        stravaActivity.Elapsed_Time__c = activity.elapsed_time;
                        stravaActivity.Event_Registration__c = registration.Id;
                        stravaActivities.add(stravaActivity);
                    }
                }
                upsert stravaActivities EventApi__StravaActivity__c.Event_Registration__c;
            }
        }
    }
    
    private static String getStravaAccessToken() {
        // TODO: Implement this method to retrieve the Strava access token from a custom setting or configuration object
        return '';
    }
    
    private class StravaActivity {
        public String name;
        public StravaAthlete athlete;
        public String start_date;
        public Double distance;
        public Double max_speed;
        public Double average_speed;
        public Integer elapsed_time;
    }
    
    private class StravaAthlete {
        public String id;
    }
    
}

to make the callout to the Strava API, you'll need to create a new Apex class with a method that will handle the callout. Here's an example of what that might look like:
 

public with sharing class StravaAPI {
    public static String makeCallout(String clubId) {
        String endpoint = 'https://www.strava.com/api/v3/clubs/' + clubId + '/members';
        HttpRequest request = new HttpRequest();
        request.setEndpoint(endpoint);
        request.setMethod('GET');
        request.setHeader('Authorization', 'Bearer ' + '[your access token]');
        Http http = new Http();
        HttpResponse response = http.send(request);
        if (response.getStatusCode() == 200) {
            return response.getBody();
        } else {
            return 'Callout failed with response code ' + response.getStatusCode() + ' and message ' + response.getStatus();
        }
    }
}

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