I just received a 0-31db attenuator with the PE4306 and OLED display from the SV1AFN. By comparison, I'll see what's going on. As I have already studied the manual of the device from which the attenuator comes, it appears to be in T although not explicit and not in π as originally I thought. Anyway, it does not change things. Worse is the SMA output jack that connects to it has often been removed out by my predecessors and does not look good. This jack is part of a handyform cable and does not bend too much. I will replace it with RG142 because the device must reach theoretically at least 12.4Ghz.
I did some tests with a 5.6dB attenuator manufactured by me: 158Ohm, 34Ohm(series), 158Ohm. I used a VNA with a single port and connected the 5.6dB attenuator in the 50 Ohm, O, S tests at 10Mhz. For 50Ohm with the attenuator connected or directly in the load there is almost no difference. S11 is in these cases -27dB. I used some cables and SMA adapters. For the other two situations, there are differences as follows. Obviously for absolute R, but these are the same as in DC measurement. S11 appears differently with the attenuator connected versus directly connected situation(without ATT). In principle, the attenuator creates an adaptation or a kind of good transfer in these two situations (ATT + SC, ATT + OC). VSWR is less than 2. It is clear for me that a VNA with two ports is required.