Congrats on upgrading to the BAT. As a long term BAT preamp owner and fan, and having recently upgraded within their line, I readily agree about the realism (inc "analogue" sound) their preamps deliver, having compared them with quite a few others.
Different people may mean or value different things which contribute to "in the room" sound. For me, one element is dynamics, where transients literally shock you, another element is spatial location and particularly a 3 dimensional stereo image with great depth discrimination and placement. Sometimes this results in instruments or vocalists appearing to hang in front of you in your listening room; on other recordings great reproduction of the hall ambience (real or studio-created) transports you out of your listening room to that hall. Across all sources, so far I have best achieved the combination of dynamics and 3 D imaging by using my successive BAT preamps with valve power amps. Contrary to both expectations and design ideology of BAT, I have done this with single ended 845 triode power amplification and sensitive loudspeakers (Coincident Technology floorstanders). I considered changing the power amplification to a balanced configuration amp (either solid state or tube) rather than upgrading my preamp and sought advice directly from Victor Khomenko (BAT’s designer) and he actually encouraged me to go with the preamp upgrade despite the Balance to single ended connection if I like the SET sound. That’s NOT to say I would rule out changing to balanced (SS or tube) in the future to facilitate a wider choice of loudspeakers if sufficient finance became available and a home demo was possible and demonstrated the benefit of the upgrade combination. The choice might also be influenced by the type of music you listen to most.
I also am convinced that on digital sources the DAC choice is very important. I see R2R seems very popular on Audiogon but I wouldn’t rush at that spec as I’ve also read of downsides. I think a home demo would be very important. In general I’m a sceptic re cables and add-on tweaks as I think there’s a lot of snake oil out there commanding high prices. However I have been convinced in my system of the benefits of a good network switch and of some cable upgrades with respect to the soundstage, dynamics and sonic detail, and that "in the room" feeling.
Being transducers (conversion of electrical signals to audio, or vice versa in the case of phono cartridges and microphones) loudspeakers, speaker-power amp matching, and speaker-room interaction (inc speaker placement) are also important for that "in the room" sound.
So in summary I think there are multiple parts of the equipment chain which help deliver what I imagine you’re after, and it is very difficult for others to predict which will have the greatest effect as a single upgrade in your system. The best way to work that out is home demo, if that’s an option for you. Nevertheless I think you’ve made a great first step for upgrading the realism of your system across all sources by upgrading your pre-amp with one from the BAT stable.
Wishing you the best on your upgrade journey, and lots of fun on the way.