sm1ma3ay There is no setting in Wurst to change or remove those log entries. They are removed in GhostWurst though.
Edit: The same is true for other log entries as well. For example, in Wurst you can't stop Fabric Loader from logging a message saying that Wurst was loaded, but GhostWurst won't show that message because it disguises itself as ModMenu. Here is a comparison:
Log file when using Wurst:
[09:17:21] [main/INFO] (FabricLoader) Loading 49 mods:
	- fabric-api 0.131.0+1.21.8
	- [many more fabric entries]
	- java 21
	- minecraft 1.21.8
	- mixinextras 0.5.0
	- wurst 7.50-MC1.21.8
[...other log entries...]
[09:17:27] [Render thread/INFO] (Minecraft) [STDOUT]: Starting Wurst Client...
[...other log entries...]
[09:18:23] [WurstUpdater/INFO] (Minecraft) [STDOUT]: [Updater] Current version: 7.50
[09:18:23] [WurstUpdater/INFO] (Minecraft) [STDOUT]: [Updater] Latest version: 7.50
Log file when using GhostWurst:
[16:05:18] [main/INFO]: Loading 48 mods:
	- fabric-api 0.131.0+1.21.8
	- [many more fabric entries]
	- java 21
	- minecraft 1.21.8
	- modmenu 15.0.0-beta.3
	   \-- placeholder-api 2.7.0+1.21.6