Social anxiety is a very real thing that countless people all around the world tend to suffer from on a more or less regular basis, and if you think that you are not the sort of person that has to deal with anything of that sort, just wait until you need to talk to your landlord. Any conversation that you need to have with the person that takes rent from you is liable to give you a nervous breakdown, especially when said conversation involves you asking them to do something that you are certain they might refuse once all has been said and is now out of the way.
However, it is absolutely critical to know that your landlord has some responsibilities that you can legally hold them accountable for, with professional carpet cleaning being one of them. The reason behind this is that apartments that come with carpets usually get higher rental payments, and landlords need to maintain the carpets otherwise the higher rent won’t make a whole lot of sense. That is why you should reference the fact that this is a requirement that your landlord is mandated to fulfill, since this would make them more amenable to your requests than might have been the case otherwise.
It can be useful to initiate this conversation with as much confidence as you can possibly muster. That will make it so that your landlord would know that you are aware of what your rights are, and they would never try to beat around the bush. You are supposed to pay for damage that you cause, but basic maintenance is the sole responsibility of the landlord all in all.