Here are some of mine:

Movies:

• 12 Angry Men, 12 jurors debate whether the defendant is guilty of murder or not. Not really competent as in professional, but rather a great depiction of overcoming differences and working together
• Ocean’s Eleven, a group of con artists working together to rob a casino
• Apollo 13, astronauts and mission control working together to overcome a life-threatening situation
• The Martian, a stranded astronaut on Mars utilizes everything at his disposal to survive until he hopefully can be rescued

TV-Shows:

• The West Wing: a president and his staff do their jobs
• Star Trek: TNG, a starship crew takes on all kinds of problems and situation as a group of professionals with a minimal personal drama

Books:

• Project Hail Mary, the protagonist wakes up on a spaceship on a desperate mission gone completely wrong and has to manage it
• The Martian: Same as the movie, a stranded astronaut on Mars utilizes everything at his disposal to survive until he hopefully can be rescued
• Red Rising Saga, the protagonist discovers the truth about his interplanetary society and does something about it
• Commonweath Saga, competent space opera, great world building
• A Fire Upon the Deep
• The Lost Fleet series, a commanding officer gets woken up after 100 years of cryo sleep in a lost escape pod to find his intergalactic society has been at war all this time and lost their competence on the way

What I didn’t like/didn’t really turn out to be competence porn imo:

• Seveness, book by Stephenson. Competent people handle a civilization ending event. A lot of competence until the author decides the plot needs some very dumb decisions. DNF.
• Theirs Not to Reason Why, book series by Johnson. A very literal Mary Sue has the ability to see the past and future of pretty much everyone among a host of other paranormal abilities. Uses her abilities to shape and save the future amid an intergalactic society. Military SF, kind of annoying at times, but still enjoyable. Currently on book 2.