PA-28-201T pilot reported turbocharger failure in cruise required a diversion to a nearby airport.

Narrative

I was flying a PA-28-201T Piper Turbo Dakota; as pilot in command. I have over 400 hours in the aircraft. My sole passenger was a private and instrument rated pilot; himself with around 100 hours in the aircraft. We were on an IFR flight plan and climbing through approximately 6;200 ft. MSL eastbound near ZZZ1. There were scattered clouds with bases around 5;500 ft. MSL up to perhaps 7;500 ft. MSL. At the moment of the incident we were not in a cloud; though many were around us.All instrumentation for the climb was nominal; showing around 35 inches manifold pressure (MAP); 2400 RPM; and approximately 100 KIAS when a loud 'POP!!!' came from the engine compartment. There was a quick shudder from the aircraft. I noted that the MAP had fallen to approximately 22 inches; though all EGTs; CHTs; and similar readings from my digital engine monitor as well as fuel flows looked reasonable. As the airspeed fell to around 80 KIAS; my passenger called out 'airspeed' and I leveled out the climb. We then maintained approximately 22 inches MAP and 100 kts. My passenger noted clouds ahead and advised that the area to our right and rear was clear. I knew that ZZZ was just behind us and so I planned on heading there. I also thought of the coincidental convenience that I know an A&P IA based at the field.I advised ZZZ Tracon. We have partial engine power and are turning direct to ZZZ airport. I intend to maintain altitude until over the field and then spiral down to land. I turned right and then direct to ZZZ. ZZZ cleared us to maintain 6;000 ft.; after which I informed them that we were VMC and we were cancelling IFR. ZZZ handed us off to ZZZ Tower; who cleared us to spiral down over the field to enter a right downwind for Runway XXR.I troubleshot the engine enroute; noting that various throttle settings would not increase MAP above 22 inches. The fuel flow rate looked nominal; temperature readings looked nominal; and the electric boost pump increased fuel flow further but did not resolve the issue. Opening the engine alternate induction air did not resolve the issue. I handed my passenger the aircraft checklist and asked him to run through the 'Engine Loss in Flight' portion to verify we did not miss any steps while I maintained a lookout for traffic. The engine was running adequately enough to maintain altitude and airspeed and we were well above an adequate glide path to ZZZ even in the event of full failure. After that sanity check on the checklist; my passenger kept his head outside to advise on glide path/route and traffic.I arrived over ZZZ at 6;000 ft. MSL (field elevation is approximately 100 ft. MSL). I executed a right spiral down to Runway XXR; hitting a High Key position over the threshold at approximately 2;000 ft. MSL. I aimed for 2;000 ft. down the runway and landed without issue.After landing; we performed a run-up. I could now get 29 inches of manifold pressure; which combined with all other indications being nominal lead me to suspect that we lost the turbocharger. (22 inches MAP maximum at 6;000 ft. MSL; and 29 inches at Sea Level.) Upon shutdown; we brought over an A&P IA that has previously worked on [the aircraft]. We removed the cowl and immediately noted that the intercooler induction air discharge line; which attaches to the intercooler with a gasket held on by a hose clamp; had detached. The engine was therefore pulling induction air from under the cowl directly by the manifold that leads to each cylinder.My A&P IA reconnected the line; checked all other hose connections for security; and verified that the turbocharger spun freely and was FOD free. We all additionally did a thorough inspection of the entire engine compartment. We performed a nominal run up; added the A&P's fresh inspection sticker to the logbook; and were on our way without further issue.I credit both my USAF 'Emergency Landing Pattern' training as well as my recent Commercial Glider Rating as factors that led to the incident as feelinglike a non-event. ZZZ [TRACON] and ZZZ Tower were both very helpful; asking if help was needed and ensuring traffic deconfliction; but otherwise making no extraneous radio calls. My passenger and I did a good job of CRM; dividing duties as appropriate and double-checking each other to maintain aircraft control; analyze the situation; and land as soon as we could.