Let's find out!
Since the beginning of the "New NHL" Era:
05/06 - Regular Season GPG: 6.16, Postseason GPG: 5.65
06/07 - 5.90, 4.95
07/08 - 5.56, 5.36
08/09 - 5.82, 5.48
09/10 - 5.68, 5.98*
10/11 - 5.58, 5.61*
11/12 - 5.46, 4.84
12/13 - 5.44, 5.02
13/14 - 5.48, 5.59*
14/15 - 5.46, 5.03
15/16 - 5.42, 5.25
16/17 - 5.54, 5.16
17/18 - 5.94, 5.90
18/19 - 6.02, 5.57
19/20 - 6.04, 5.47
20/21 - 5.88, 5.48
21/22 - 6.28, 6.31*
22/23 - 6.36, 6.28
*Playoff games were higher scoring than regular season games
Now let's see whether Stanley Cup champions were offensively or defensively oriented:
05/06 Hurricanes - 3rd in regular season GF, 18th in regular season GA (Offensive)
06/07 Ducks - 6th GF, 7th GA (Balanced)
07/08 Red Wings - 3rd GF, 1st GA (Balanced)
08/09 Penguins - 5th GF, 18th GA (Offensive)
09/10 Blackhawks - 3rd GF, 5th GA (Balanced)
10/11 Bruins - 8th GF, 3rd GA (Balanced)
11/12 Kings - 29th GF, 2nd GA (Defensive)
12/13 Blackhawks - 2nd GF, 1st GA (Balanced)
13/14 Kings - 25th GF, 2nd GA (Defensive)
14/15 Blackhawks - 16th GF, 2nd GA (Defensive)
15/16 Penguins - 3rd GF, 7th GA (Balanced)
16/17 Penguins - 1st GF, 17th GA (Offensive)
17/18 Capitals - 9th GF, 15th GA (Offensive)
18/19 Blues - 15th GF, 6th GA (Defensive)
19/20 Lightning - 1st GF, 9th GA (Offensive)
20/21 Lightning - 8th GF, 6th GA (Balanced)
21/22 Avalanche - 3rd GF, 7th GA (Balanced)
22/23 Golden Knights - 14th GF, 11th GA (Balanced)
(For the record, the 23/24 Jets were 15th GF, 1st GA.)
So I was pretty wary (and weary) of all the Jets play "playoff style hockey" (ie, the right way) narratives during the regular season. Aside from the early 2010s LA Kings, has anyone really won that way? Is it a sign of a true Cup contender to win all a bunch of 2-1, 3-2 games in the regular season? Considering that defence-first teams tend to rely on superior goaltending and/or work ethic, I'd say no, that most true Cup contenders are those that can (to some degree) coast through the regular season and win games through sheer talent, but have the necessary discipline to lock down and win 2-1 and 3-2 games when necessary. The Avalanche and Oilers can go places where the Jets and Kings can't. (The 2012/14 Kings are obvious exceptions here, as they had the perfect personnel to play that style.)