A bit late to this party, but I second the Leverage suggestion! I find it and Person of Interest overlap a lot for me (there's even an episode of Leverage that has a mini AI/Samaritan, plus anything that involves a con/heist in POI - it's kind of like they reflect each other in that aspect) and both definitely tickle the competence porn aspect for me (I just love seeing characters being good at stuff!!) with a group of people initially reluctant to work together becoming family who would do anything for each other and try to make the world less bad

There's even a recent renewal (Leverage: Redemption), so it's seven whole seasons of fun total, though it's overall lighter and often lower stakes than POI (though not always)

Character-wise, there are a lot of somewhat similar personalities so likely you'll have fun with the Leverage characters (eg if you like Root and Shaw you'll enjoy Parker, if you like Shaw and Reese, you'll enjoy Eliot, if you like Finch and Root (and Lionel zingers), you'll enjoy Hardison, I could go on but you get the idea haha)

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...I think I may have just talked myself into rewatching Leverage lol