It has been some time since HONK was actively developed, but it is still unmatched for lightweight 2D PNGtubers with phoneme detection because it uses Oculus LipSync (which is unfortunately also end of life.) I was having a terrible time with phantom talking using HONK 3.0.2a latest (the issues were not fixed by using the stable version.)
***If you don't want to deal with this and are looking for an alternative to HONK until such time as it might be picked back up by the developer, PNGTube Remix is the only other lightweight 2D vtuber software I could find with phoneme detection and it's pretty funky to set up but it is there.***
After reading through some of the suggestions on here and having little success I finally think I found some tweaks that should help, at least if you are running HONK on Windows 11. When I switched to a 2 PC setup for streaming, my encoder PC uses Win11 and I started having issues with HONK.
***I had no issue running HONK 3.0.2a nor stable on my Windows 10 computer, even when running a game and encoding to stream, but these suggestions may help if you have having trouble there as well.***
1) Run HONK as administrator (set it to ALWAYS run as admin by navigating to the exe in the honk-win folder, right click>Properties>Compatibility>Check "Run this program as an administrator".) This will be annoying because it will prompt you to "allow this program to make changes to your computer" unless you turn off those notifications, which is not particularly good practice. ***This may be all that is needed to reduce or eliminate phantom talking for you, if not, please continue.***
2) Run OBS or your streaming software as administrator (see steps and warnings above.) By running these programs as admin, it prioritizes the processes, and significantly reduced the "phantom talking" issue for me.
3) Turn off all unnecessary programs and minimize to taskbar any required programs which render video previews if possible.
Something I noticed was that HONK would run poorly (making phantom talking worse or simply not recognizing speech as quickly/as accurately) when I was asking a lot from my encoder PC by having a lot of programs running at once. In one notable example, if I am using Spotify while streaming I get noticeable recognition lag from HONK, even if it's the web browser version. That input lag was reduced (but not eliminated) when the Spotify app or web browser version were MINIMIZED or closed.
I'm still doing more testing, most of this is based on tweaks I did when NOT streaming. Did some tests encoding to a recording instead and I'll report back after some streaming tests if there's more to be done here.