As James Wirz correctly deducted in his answer, the story I was looking for is called "Stranger's eyes", by Russian Author Dmitri Bilenkin (Дмитрий Биленкин). Originally published under the name "Чужие глаза" in 1971. Published in the English collection "The Uncertainty Principle" and in the German collection "Fluchtversuche" (where I probably first read it).
I found a used copy of the book to confirm that this is indeed the correct story. Here are some quotes matching the details from my question:
The planet is covered by a thick cloud layer and orbits a dim red star.
The sun was no brighter than cast iron, and the planet itself was even duller. Compared to the flat disc of the planet that we could see, the blackness of space seemed to concentrate light.
The humans start exploring the planet from orbit, meticulously abiding by a non-interference protocol.
The rule book for uninhabited planets is large enough to kill a man, but it is nothing compared to the one for planets that have life, and perhaps intelligent life. And you can be sure that Zibella followed it to the letter.
The captain is a real stickler for the rules, ...
There wasn't another captain as punctilious as Zibella in the entire
cosmos. It was a standing joke that his reason for not marrying was
that there were no instructions governing the procedure.
... making sure that any active scans are only employed after the crew have verified that no electromagnetic emissions come from the planet
The regulations were obeyed unswervingly: the communications activity of the scouting party must correspond to the communications level of
the planet. In simple terms, this meant we had to make sure that the
planet didn't even have the simplest, most primitive transmitters and
receivers that could intercept our signals and therefore discover us
before we wished to be discovered.
the inhabitants act strangely: they all seem to lack optical senses, but exhibit behaviour that suggests they would normally have such senses.
it stood for a while and headed down the path with its free hand. Could this creature, feeling its way along the path, have dug up the fields surrounding the settlement? Build the houses? Hunted? It was impossible to believe.
For instance, they repeatedly bump into obstacles or stumble over cliffs.
It took a step. Into the void. Even as it fell, it did not drop the vessel of precious water. We heard a scream. What we didn't want to believe was true. This world was blind, but it had gone blind recently.
It turns out that the frequency of the crew's active scans — implemented at one of the few frequencies that could penetrate the cloud layer — was also the frequency used by the aliens to see. Due to the much higher energy of the scans compared to the dim sun, all of the inhabitants were blinded by the scans.
Our computer had picked the frequencies for which the atmosphere was most transparent and which were for that reason the "life light" on the planet. But our equipment was less sensitive than the inhabitants "eyes," and we wanted to see as well as possible. And so the locators burst into blinding light.
I saw the black planet where we would have to spend many long years salvaging what could be saved. The thought of the depressing hell that awaited us, strangely enough, brought me relief.