It requires more exertion to reach the oxygen depletion level that
causes the jump to a higher heart rate, you mean.

For roughly a month I've been training below 70% of HRmax and recently I
observed, that my heart rate during relaxed pedaling is significantly
lower
than it used to be a month ago. I wonder if it's just a normal, let's say,
adaptation, and my aerobic capacity has increased

This is the usual interpretation, as I understand it.

Most riders would view this as an achievement.

Ok, but even when riding il relativly slow leisurely pace, I feel
exhaustion, despite not having reached 70% of my HRmax. I don't feel
comfortable with that.

Lechu