how do i use user's ID for matching it with a condition so that when the user sends message to channel, the bot can do specific tasks for the user

I have tried:

if message.channel.category.id == 774267322687815710:
  if user.id == 415884831805931551:
      await message.add_reaction("🔥")

I have tried this but seems like I cannot make it work for the message that is being sent by the user, it only fetches the user's id

You have to get the author of a message instead of just user.id as you also have not defined user.

Have a look at the following event instead:

@client.event / @bot.event / @commands.Cog.listener # Depends on what you use
async def on_message(message):
    if message.channel.category.id == CategoryID:
        if message.author.id == UserID: # Get the ID of the AUTHOR
            await message.add_reaction("🔥") # If the ID is correct
        else:
            return # If the ID is incorrect/does not match do nothing

You maybe also want to take a look at the docs