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Getting the Chinese to agree to send a mission to London can't be viewed as a success for McCartney because it just utterly fails to achieve anything McCartney was actually sent to get.
It may not be viewed as a success in London at the time, but it would be something to build on which could produce a successful historical outcome.
First of all the Chinese never entertained permanent foreign embassies. The very concept was foreign. You want to get to know someone, pay a few visits, not ask for a room in his house. McCartney basically crashed the emperor's big birthday party and then refused to do the customary kowtow. Qianlong decided to act graciously, probably the way a host would still welcome uninvited guests at his daughter's wedding. But then MaCartney started asking for a place to stay permanently and that annoyed Qianlong

. Besides Qianlong was very old. He was 80, ancient in those days. He had ab incredibly successful career and in his old age lost interest with running the show. He was just not in the mood to try something risky. A sign of respect would be to exchange embassies. That I think was doable.
The Chinese viewed everyone else as barbarians, including the Manchu rulers. Referring to someone as barbarian is like Jews calling others gentiles. It doesn't automatically imply that nation is unworthy of diplomatic relations or respect. The Chinese frequently sent emissaries abroad, and Qianlong in fact did have Europeans (Jesuits) at court, as his father Yongzhen and his father Kangxi before him. In fact Manchu Emperors were huge Europhiles. Yongzhen likes to play dress up in European clothes and wigs. Qianlong had an entire Western theme place built by a Jesuit architect. It was all Italian style carved marble and had a faux European village for the emperor to visit by boat.
Maybe if Macartney was Italian, Qianlong would've been more impressed

. But Qianlong didn't know much about the British. Not one of his courtiers have ever been outside the Sinosphere. The British were not a land power which to Qianlong meant they were small and insignificant. They couldn't have a large population and tax base. Traditionally Chinese understood northern barbarians as important land powers but had little respect for those that come from the south seas. As far as he was concerned the British were little more than common sea going traders like the East Indies natives. He felt he was being a pretty gracious host giving Macartney plenty of supplies and gifts for his trouble.
Britain had to start with establishing its bona fides. It would make a difference if some Chinese were actually able to go to Europe and see it for themselves. It's sometimes hard for us to imagine what its like to live in a world where some countries are so far away and foreign that not one of your people have ever been there and back. Without some basic understanding of who the British were and what they had to offer, what Macartney was asking for was beyond what Qianlong was capable of understanding. It's one thing to ask for too much when everyone understand each other. But when they know next to nothing about you and you ask for the sky, there's not going to be a negotiation. The goals of the MaCartney mission was unrealistic and doomed from the start.