ctx.guild.id
returns an integer type data. In your code, you tried to compare it with a string. You just have to delete the quotes. Then, you cannot add role with the role's id. You have to add the role's itself.
@client.command()
async def addrole(ctx, member : discord.Member, role : discord.Role):
if ctx.guild.id == 777563438469087244:
await member.add_roles(role)
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