Hi Oliver,
Welcome!
I can’t speak to climbing specifically, but I can provide guidance on base training in general.
As you have already guessed, at the early stages of aerobic base training, the activity itself is not as important as the duration and the HR. The first step, if you haven’t already, will be to determine your AeT. You will want a HR chest strap and monitor to get accurate results. Unfortunately, even the best sports watches are not going to give you an accurate enough HR measurement. Most straps can be paired to an app if you don’t want to also buy a watch (if you don’t have one). These articles provide information on how to do the aerobic threshold self-assessment, as well as a how-to video:
The next step is to programme enough regular aerobic base training (in zones 1 and 2 — i.e. BELOW AeT) to move the needle. If you can manage it, five days a week would be ideal, total time in motion 3+ hours, and progressing at a rate of no more than 10% per week, with a regularly scheduled recovery week at 50% of the prior week’s volume (3 weeks build, 1 week recovery is typical).
Since your overall goals involve bipedal motion (approach hikes, alpinism), you could start with sport specificity right at the beginning, using walking, hiking, running for your base training. One thing to be aware of is that, depending on your AeT, you might need to start with walking and hiking and progress to running. Or maybe you can run on completely flat ground (like a track), but have to walk if there’s a gradient. That’s what I had to do in the beginning. Rowing and swimming would also be good. Swimming is particularly good as a recovery workout. Rowing would give you some upper body strength work for climbing, but you’d have to carefully monitor your HR.
I hope this helps. Let us know if you have further questions.
Jane