What is going on is that by adding attenuation you are increasing the noise figure (NF) of the receiver. NF is the amount of internally generated noise in the receiver channel prior to detection.
In a perfect world there would only be thermal noise, which is always -174 dBm/Hz. In a 2.7KHz passband (remember, the S-meter is measuring noise in the entire passband, so 2700Hz worth of noise) there would be -174 + 10Log(2700) of noise, or -174 + 34 = -140dBm (about S1).
In the real world the radio adds it's own internally generated noise from both passive components like attenuators and active components like LNAs, preamps, and other amplifier stages.
With the 6M LNA turned off, the NF of our radios is right around 15dB. With the 6M LNA turned on it's closer to 1dB.
Sadly, we'll never see that level of performance (only 1 or 15dB added to the thermal noise floor) except on the test bench because the atmospheric noise at the antenna is already worse than that. However, by adding attenuation in the receiver path, especially prior to the first amplifier, and especially a large amount of attenuation (e.g. 30dB) you will definitely see an increase in the noise floor, and this is totally normal and expected.
Note that calculating the receiver noise figure is not at all straightforward. Each passive and active stage must be analyzed using something called "cascade analysis". The first amplifier in the cascade will dominate the results. Attenuation prior to that amp will have moderate influence. Everything after the first amp will have minimal influence.
There are a lot of cascade analysis calculator web sites out there. I like this one because it is quite comprehensive:
https://www.qorvo.com/design-hub/design-tools/interactive/cascade-calculatorNote that with your masthead LNA you'll want to disable the internal 6M LNA in the ANAN. Just out of curiosity, what make/model is the masthead LNA?