I experimented a little more and see it doesn’t matter if I have the power pins in battery or programmer mode.
The same happens.
If the programmer is idle - module just plugged in - voltage is stable around 3.02v. But when I start debugging it increases to 3.5v, peaks as high as 3.56v
Two pcs 1448 diodes in series solved that. Now programming voltages are just below 3v.
Now, the other programmer I have also is a kitprog2, but the board has a slightly different layout, D1 is located on the top side. Anyway, is appears to have the same connections so I assume it will be safe to mod that one too.