Commercial Fixed Wing
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Communication Breakdown; Situational Awareness; Workload; Time Pressure
ATC Issue All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Overrode Automation
Staffing; Human Factors; Environment - Non Weather Related
We were being vectored to final for the visual to Runway XXR in ZZZ. Descending out of 9;000 feet in the right downwind of the ZZZZZ arrival we were then given a vector 'Turn right heading 030; descend and maintain 7;000 feet.' It was clear that the Controller was very busy and was working approach for three parallel landing runways with many inbound flights that morning. Our next instructions were; 'Turn right heading 090.' Shortly after the turn to the east we were assigned; 'Turn right heading 150 to join the [Runway] XXR LOC.' This last instruction was given a minute too late. It was already apparent that we were going to fly through the final approach course with parallel traffic joining up for [Runway] XXL. The Captain had been saying prior to this; 'Controller needs to gives us the turn... Controller needs to turn us already... we are going to fly through final.' Sure enough the turn was way too late and the aircraft automation was too slow to make the tight turn. The Captain immediately informed ATC that the vector was issued too late and that we would be flying through the final approach course and correcting west bound to rejoin. I disengaged the autopilot as the automation was not reacting fast enough to recapture the final approach course. ATC then issued us a 190 heading to rejoin the localizer and a traffic advisory to the aircraft that was flying the parallel; saying we were at their 3 o'clock same altitude and correcting west to rejoin [Runway] XXR LOC. Just seconds after the heading to rejoin was issued (We were already in the turn at this time) a TCAS Traffic Advisory went off due to the proximity of the aircraft on the [Runway] XXL parallel visual. Nothing further happened from this event. We were able to rejoin the [Runway] XXR LOC maintain 7000 feet until descent for landing was necessary and we completed a stabilized approach to landing.The cause of this event was due to task saturation for the Air Traffic Controller. Controller was working one approach frequency with dozens of aircraft needing vectors to final for the triple parallel visuals landing south at ZZZ. The automation lag didn't help when trying to join the LOC with the last second instructions however that was mostly mitigated by disconnecting the autopilot and hand flying a more abrupt turn to re-intercept and avoid further deviation.As a pilot (and never having been in to see a behind the scenes look at an ATC approach facility) I cannot tell you exactly what was going on or any; if at all; distractions may have existed behind the microphone at ZZZ Approach that morning. However; I can tell you based on my perception that the controller was talking non-stop with zero breaks between Controller and aircraft transmission and that Controller may have been overloaded during this event.
Air carrier First Officer reported the ATC Approach Controller seemed overloaded with arriving aircraft and gave the heading change for localizer intercept too late.