Roland AE-20 Aerophone Digital Wind Instrument
I've tried a "cumbersome" and expensive sax mute first but that didn't work out to well for me.
I've decided to get the Aerophone AE-20 then to try to boost a bit my work on scales, arpeggios and melodies and so far it's serving me well. After dinner I can consistently get not 1 to 2 hours of practice in my living room without disturbing anyone. Then when I can I pick my saxophone and I can focus on my tone production and embouchure without without thinking too much about which note to push next in an arpeggio or a scale. After a couple of days I got used to the Aerophone different key feel and sensitivity and I can say I enjoy practicing on it. The main downside of it is that if you're running it on batteries you have to take them out to recharge them and also you cannot power it from the USB-C port but only via the provide DC adapter.
Overall I'm satisfied with it and hopefully I will start to use it in more "artistic" ways once I'll be a more proficient player.