A run/walk approach for most of your runs is absolutely reasonable. Early in my most recent training cycle as I was building up mileage, I used the run/walk on all runs other than my planned-fast workouts to help me keep my HR under a specific level. Just like accepting that going up hills slow is the right approach, a run/walk mix might force swallowing the ego a bit but it’s smart. If going 10K requires a run/walk mix given your current fitness levels, I see zero problems with that.

Understand and accept that whatever your goals, this is likely to be a long-term process, but improvement absolutely will come and it feels tremendously satisfying.

Generally it means that I am watching/using my HR measurements (as told to me by my trusted Garmin watch) during training runs much more than I used to. In practice, this means:

1. (Most relevant to this thread) I have an additional source of info to guide my “constant effort on hills” strategy. I think I already knew that I was previously pushing much harder up hills, but when I really focused on HR and saw how much it skyrocketed on uphills it became even more clear that perhaps my ego was encouraging me to go harder than I should.
2. I’ve done more “low heart rate” training. You can find lots of info out there (including on Reddit) about this, but it goes with the general idea that most training should be relatively easy and the value comes from simply building up the mileage. A corollary of this is the idea that many runners are pushing too hard too often and put themselves at risk for injury and burnout (or for beginners, perhaps giving up running entirely because it’s hard to habitually do something that’s hard).
3. It’s another source of info that guides me on days that are perhaps off-days and a sign I should take it easy. If I start a familiar run and see my HR is higher than I would expect, I usually trust the implicit message and cut down on pace or distance for that run.
4. I’m sure there are other things I’m forgetting, but knowing my HR is now just a fundamental aspect of my self-monitoring when running.