What workout best combines with outside training to improve climbing?

It’s still very difficult to be specific, because I don’t know what outdoor training you’re doing, how long those rides are, and how intense.

Bearing that in mind, I would base your training around Sustained Power Build.

https://www.trainerroad.com/cycling/plans/158-sustained-power-build-mid-volume

The 2 important things are (1) to raise your FTP so you can climb faster, and (2) to increase muscle endurance so you can do long intervals without fatiguing.

I would do at least 2 of the workouts on Tuesday, Thursday, and Saturday indoors. You can do a decent version of Wednesday and Sunday outdoors, even if you don’t do the exact intervals, they’re basically endurance and tempo. And maybe you could do one of Thursday or Saturday outdoors, if you have a long steady climb where you can do the intervals at the right power.