This thread and this thread by @geo_c are interesting.
Interestingly, it is possible to do the same thing in Fatdog, without using pipewire. Instead, we can use the real JACK server (which is included in the base).
In Fatdog 901 you can do this with aloopd. All you need is to launch JACK server using qjackctl, and configure Fatdog to use aloopd. In aloopd's configuration, then configure it to run with JACK bridge. In this mode, aloopd will auto-connect any ALSA apps (e.g. browser) to JACK output automatically. You can then modify the connection using qjackctl to insert the various JACK filters as discussed in geo_c's posts.
But this is a temporary connection and when then ALSA app stops the sound, the connection is lost and when you start the music again, you will have to re-do the connection (not much, only two ports need to be re-configured in the qjackctl graph, everything else stays).
In next iteration of Fatdog (whenever it is released), it will be possible to setup a permanent connection for ALSA apps, so we can save and load the connection again at next start. In fact you don't have to wait for it, because it's so very easy to do it. It can be done manually, or I can post the updated aloopdcfg.sh, if any of you are interested.
It's really nice to be able to pipe the output of freetube through Calf's equaliser and limiter, for example (screenshot attached). In this particular setup, the JACK processing load is less than 8% (that's using buffer size of 64). Everything is very smooth even though I'm only using Fatdog standard low-latency kernel (not RT kernel). And this is on an old 2018 laptop.