Will an Amp change improve my system ?

I agree with @audphile1, I would go with a bit more horsepower, even if you don’t listen at higher volumes. I own the Coda #8 v1, and while I have not heard the PS Audio amp, I feel it would be a significant upgrade. 

“WiiM pro ( a great device for $149 !)”

Agreed. Recently purchased one of these. It works great with the Plex server-App. Highly recommended. 
 

Which mode is used the most on the Freya+? Tubes or the others?

A note, on your list are radically (!) different sounding amps. The Pass will be very natural sounding, and perform as if it has much more power than the specs would suggest. I think it would be an excellent choice to help your system be much more musical. On the other hand Benchmark (or the Luxman to a bit lessor extent)is highly detailed oriented and is going to reinforce the leanness of the other components in your system. One of the big differences in better systems is they can be more fleshed out and sound much more natural sounding. The CODA will be in between. If you like a very detailed analytical and a strong bass slap (somewhat artificial) the the Benchmark Luxman side, CODA in the middle as is the Rouge (although it is tubed… it doesn’t have the refinement of better tube designs) or the Pass for more musical and natural.

I prefer nartural and musical sound that is still detailed, not in your face, but laid back with a deep - wide sound field… I’d choose the Pass. I had a Pass amps for several decades.

I have the 30,2 40th anniversary (almost the same as the XD) and matched it with a Pass Labs XA25. It is a match made in heaven. Don't know about your room size but, it is plenty for mine of 20x12. If you want some info about the combo, please check Herb Reichert's review in Stereophile Mar 2018. The interconnect is a RCA Cardas Rev1 and a good match with the Pass. I have tried different stands and highly recommend the Ton Trager. More expensive but  it makes Shaw's cabinets sing because of their resonance configuration. Keep us posted about your choice for a new amp.

The S300 is a fine amp for the price, but for me the Pass was much better sounding...don't know your speakers though...some love Benchmark, but very many do not...