Thanks!
I had investigated the issue from top to bottom, and it seems that for some reason an post metadata is triggered to update and the search tries to re-index that post during the trigger, because this option was activated.
It should be fine, but in this case rendering the block during that event very likely fires a hook, which should be used later, and then it’s not rendered correctly anymore. Anyways, I have deactivated that option, now it’s all right.
I tried to look for a possible way around to have that feature active as well as bypassing the issue, but it’s not possible as I don’t know what hook fires exactly, and it’s better not to fiddle with it, it may cause even more problems.
Luckily this is not a bug for fixing, so this should resolve it permanently.