Fabric reauth doesnt work on 1.16.3. It launches the game but if you press reauth button in multiplayer menu your game crashes.

Description: Rendering screen

java.lang.IncompatibleClassChangeError: Expecting non-static method technicianlp.reauth.gui.AuthScreen.method_25300(Lnet/minecraft/class_4587;Lnet/minecraft/class_327;Ljava/lang/String;III)V
at technicianlp.reauth.gui.AuthScreen.method_25394(AuthScreen.java:94)
at net.minecraft.class_757.method_3192(class_757.java:824)
at net.minecraft.class_310.method_1523(class_310.java:1023)
at net.minecraft.class_310.method_1514(class_310.java:656)
at net.minecraft.client.main.Main.main(Main.java:215)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
at java.lang.reflect.Method.invoke(Method.java:497)
at net.fabricmc.loader.game.MinecraftGameProvider.launch(MinecraftGameProvider.java:192)
at net.fabricmc.loader.launch.knot.Knot.init(Knot.java:140)
at net.fabricmc.loader.launch.knot.KnotClient.main(KnotClient.java:26)

The same issue also happens on 1.16.2

1.16.2 should work with the 1.16.2 version of the mod (available here: https://www.curseforge.com/minecraft/mc-mods/reauth-fabric)
Same is likely the case for 1.16.3 but that requires a rebuild

Should this be extended to 1.16.4, which changed the auth system it seems?

No the 1.16.4 Crash was unrelated to this one and caused by a change in the authlib.
This Issue has already been fixed in a previous version.