I just logged into Strava desktop site to check - I’ve got 371 KOMs at present (plus a load of joint 1st that don’t even appear in your records). Based on how it is where I live, you need good 00:30 - 3:00 minute power. That’d be anaerobic and VO2 max workouts if you wanted to use TR to train for KOMs. I’m doing something like this at the moment to attempt to try and raise my aerobic ceiling as my FTP is quite a high % of my best 5 minute effort. It hurts - a lot. If you’re new to this, I wouldn’t do more than 1 a week to start with, but you could work up to 2 a week.
Edit: TR Z5 and Z6 rides will certainly help, and make you able to hit a better repeatable power. However after thinking again, most 2:00 and under KOMs tend to be unsustainably hard efforts, so do some all-out sprints as well. The type of sprint that leaves you ready to collapse at the side of the road is ideal!
I became very anerobically inclined chasing KOMs all the time up until about 9 months ago. My goals have moved on from chasing KOMs (nothing wrong with it IMO) and I’m more interested in becoming a better, more rounded cyclist. To that end @mcneese.chad has laid out the best advice already. By having a better FTP it becomes easier to be faster across the board.