Looks like the first mod in your current load order includes an older version of Harmony (or at least one of its dependencies), which breaks all mods built on a newer version (which includes Basemod, but also a lot of other mods).
Go into Basemod's dll folder (Mods\2603522001\Assemblies) and copy 0Harmony and all files starting with Mono to the offending mod's dll folder (Mods\2870870361\Assemblies). That should fix it.

I tried what you said and it didn't work, so I just uninstalled that new mod and reinstalled BaseMod, but these doesn't fix the game and mods.
Here's Player.log after I uninstalled the mod, reinstall BaseMod seems not changing it.
https://pastebin.com/E7vPzwb6
Do I tried to reinstall every other mods or I've already broke something else?

What are BepInEx files doing in your Basemod folder? Namely, 0Harmony20, HarmonyXInterop and three files starting with BepInEx. They shouldn't normally be there.

I downloaded BaseMod from Nexus and see they were put in the same folder, so I thought they were the file missing.
Anyway, I deleted most of the files both vanilla and workshop and redownloaded them through Steam to make sure they were clean as before I messed with the file.
But BaseMod still not working after that, it seems that System.MissingMethodException: Mono.Cecil.MethodDefinition MonoMod.Utils.DynamicMethodDefinition.get_Definition() is the problem now.
Player.log: https://pastebin.com/bbKDSnF1
Thanks for the reply and answer.

Yes, it seems that the problem is with MonoMod.Utils. Could you check if you have any files with this name in your game (vanilla) folder?

I found one shortcut called BaseMod for Workshop in
Library Of Ruina\LibraryOfRuina_Data\Managed\BaseMod MonoMod.Utils is in that BaseMod, but this is through a shortcut, did that matter?

It shouldn't matter, only files that are actually in the directory matter.
Another thing you can try is to start the game once while disabling everything other than Basemod (no need to continue, you just have to get past the mod menu and into the main menu), then restart and enable the rest back.
Also, are you using the most recent version of the game?

Game version is 1.1.0.6a13.
I tried enable only BaseMod and that went normally, but after enable other mods back it still have the same error log and BaseMod back to not working, I guess I'll need to trying the mods one by one now?

Curious. Could I trouble you to do it again, this time uploading Player.log both from after the first launch (with just Basemod) and from after the second launch (with other mods)? Also, please do the same with ModSetting.save (though it's better uploaded to a general filehost instead of text-only).

Player.log with only BaseMod: https://pastebin.com/uyVnXsYY
Player.log with other mods enable: https://pastebin.com/dPvMKpFp
ModSetting.save: https://imgur.com/a/q3vsNuv
ModSetting.save is just look totally same, and I notice you want filehost instead of text after I upload these, I'll trying that next time.

...oh, it seems like the latest version of Basemod disabled the latter half of its priority changes... for whatever reason. Anyway, try using this ModSetting.save instead (you'll have to re-enable all other mods you have): https://files.catbox.moe/4as4gd.save

It's fixed now, thanks a lot for these helps.
Did I break BaseMod or just the update did it, I want to know can I still adds new mod from workshop?

Yes, you can still add new mods.