None of my commands are running on discord.py and I'm not sure why

import hikari
# also import lightbulb, that works with hikari
import lightbulb
import discord
from discord.ext import commands
import os
from help_cog import help_cog 
from music_cog import music_cog

# intents : or you pick default(), or you pick all()
# but you have to modify your bot Gateways intents in discord portal accordingly
# since .all() requires to aknowledge all intents possible. 

intents=discord.Intents.all()

# now you want to define your token here, before passing it
# assuming you have a file ".env" in the same folder as your application

TOKEN = os.getenv('DISCORD_TOKEN')

# then you create your bot. Lightbulb is going deeper than hikari 
#since you can configure the command prefix aswell so.. 
# bot = hikari.GatewayBot(token=TOKEN, intents=intents)
# turns into : 
bot = lightbulb.BotApp(token=TOKEN, intents=intents, prefix="!")
bot.remove_command('help')

async def setup(bot):
    await bot.add_cog(help_cog(bot))
    await bot.add_cog(music_cog(bot))

bot.run()
#token isn't needed here since you use hikari/lightbulb that manages it

In the other file it should go this way :

import hikari
import lightbulb
import discord
from discord.ext import commands

from youtube_dl import YoutubeDL

class music_cog(commands.Cog):
   def __init__(self, bot):
       self.bot = bot

       self.is_playing = False
       self.is_paused = False


       self.music_queue = []
       self.YDL_OPTIONS = {'format': 'bestaudio', 'noplaylist': 'True'}
       self.FFMPEG_OPTIONS = {'before_options': '-reconnect 1 -reconnect_streamed 1 -reconnect_delay_max 5', 'options': '-vn'}

       self.vc = None

def search_yt(self, item):
   with YoutubeDl(self.YDL_OPTIONS) as ydl:
       try:
           info = ydl.extract_info('ytsearch:%s' % item, download=false)['entries'][0]
       except Exception:
           return False
   return {'source': info['formats'][0]['url'], 'title': info['title']}
   
   def play_next(self):
       if len(self.music_queue) > 0:
           self.is_playing = True
           
           m_url = self.music_queue[0][0]['source']

           self.music_queue.pop(0)

           self.vc.play(discord.FFmpegPCMAudio(m_url, **self.FFMPEG_OPTIONS), after=lambda e: self_play())
       else:
           self.is_playing = False

   async def play_music(self, ctx):
       if len(self.music_queue) > 0:
           self.is_playing = True
           m_url = self.music_queue[0][0]['source']

           if self.vc == None or not self.vc.is_connected():
               self.vc = await self.musoc_queue[0][1].connect()

               if self.vc == None:
                   await ctx.send('could not connect to the voice channel, sorry Blooketeers')
                   return
           else:
               await self.vc.move_to(self.music_queue[0][1])

           self.music_queue.pop(0)

           self.vc.play(discord.FFmpegPCMAudio(m_url, **self.FFMPEG_OPTIONS), after=lambda e: self.play_next())

       else:
           self.is_playing = False

# here, it's not commands.command but bot.command
# but we also want lightbulb to take over this, so we remove overwrite
@bot.command
@lightbulb.command("play", description="play the selected song chosen by the Blooketeers!")
@lightbulb.implements(lightbulb.PrefixCommand)
   async def play(self, ctx: lightbulb.Context, *args):
       query =' '.join(args)

       voice_channel = ctx.author.voice.channel
       if voice_channel is None:
           await ctx.send('connect to a voice channel blooketeers!')
       elif self.is_paused:
           self.vc.resume()
       else:
           song = self.search_yt(query)
           if type(song) == type(True):
               await ctx.send('Sorry Blooketeers, I couldn\'t download the song. Incorrect format, try a different keyword.')
           else:
               await ctx.send('Song added to the queue Blooketeers! Happy listening!')
               self.music_queue.append([song, voice_channel])

               if self.is_playing == False:
                   await self.play_music(ctx)
# here too 
@bot.command
@lightbulb.command("pause", description="Pauses the current song chosen by the Blooketeers!")
@lightbulb.implements(lightbulb.PrefixCommand)
async def pause(self, ctx: lightbulb.Context, *args):
       if self.is_playing:
           self.is_playing = False
           self.is_paused = True
           self.vc.pause()
       elif self.is_paused:
           self.is_playing = True
           self.is_paused = False
           self.vc.resume()
           
# and here 
@bot.command
@lightbulb.command("resume", description="Resumes the current song chosen by the Blooketeers!")
@lightbulb.implements(lightbulb.PrefixCommand)
async def resume(self, ctx: lightbulb.Context, *args):
       if self.is_paused:
           self.is_playing = True
           self.is_paused = False
           self.vc.resume()

# and here 
@bot.command
@lightbulb.command("skip", description="Skips the current song chosen by the blooketeers!")
@lightbulb.implements(lightbulb.PrefixCommand)
async def skip(self, ctx: lightbulb.Context, *args):
       if self.vc != None and self.vc:
           self.vc.stop()
           await self.play_music(ctx)
# and here 
@bot.command
@lightbulb.command("queue", description="Displays all the songs currently in the queue Blooketeers!")
@lightbulb.implements(lightbulb.PrefixCommand)
async def queue(self, ctx: lightbulb.Context):
       retval = ''

       for i in range(0, len(slef.music_queue)):
           if i > 4: break
           retval += self.music_queue[i][0]['title'] + '\n'

       if retval != '':
           await ctx.send(retval)
       else:
           await ctx.send('No music in the queue Blooketeers, go add some!')

# and here 
@bot.command
@lightbulb.command("clear", description="Stop the current song and clears the current queue Blooketeers")
@lightbulb.implements(lightbulb.PrefixCommand)

async def clear(self, ctx: lightbulb.Context, *args):
           if self.vc != None and self.is_playing:
               self.vc.stop()
           self.music_queue = []
           await ctx.send('All the music is cleared Blooketeers, go add some more!')

# and finally here
@bot.command
@lightbulb.command("leave", description="Kicks the bot from the voice channel Blooketeers!")
@lightbulb.implements(lightbulb.PrefixCommand)
   async def leave(self, ctx: lightbulb.Context):
       self.is_playing = False
       self.is_paused = False
       await self.vc.disconnect()

I am not completely sure it will work, as said in previous comments, I never used hikari/lightbulb, but following their doc, it seems to be the way. I've added comments where I changed/added items.