Because this has seemingly become my specialty lately, let's talk about the effects this will have on the Qing.
What’s the long term effects of British America on Asia?
American merchants will be clamoring for the revocation of the BEIC's monopoly on British trade in India and China. IOTL, there was already pressure in the empire from independent merchants for the government to revoke the BEIC's monopolies, and the India monopoly was revoked when the BEIC's charter was renewed in
1813, and the China monopoly was revoked when it was renewed again in
1833. The result was a huge flood of opium into the Chinese market by hundreds of independent merchants, which forced the previously unattentive Chinese government to make a formal response, which provoked the First Opium War.
IOTL, American merchants accounted for around 10% of the opium smuggled into China by 1813, so they'll certainly put additional pressure on the British government to break the BEIC's monopoly ITTL. In fact, it's entirely possible that the BEIC's monopolies will be repealed in the 1793 and 1813 charters instead of the 1813 and 1833 charters. Hell, they might even repeal both the India and China monopolies
in the same charter in 1793, which would cause the flood of opium and the resulting response to come 3-4 decades earlier than IOTL. This would also have huge effects on India and Burma, but I won't go into them here.
Effects:
1. Opium smuggling into Canton rises earlier, forcing the opium issue to the top of the Qing list of priorities 20 years earlier than IOTL. This has major implications, because this gets the opium crisis started
before the Spanish New World colonies declare independence and
indirectly cause an economic crisis in China lasting from the mid-20s to the mid-40s. Besides the obvious potential for an earlier Opium War, this has a major effect on how the Qing government thinks of the crises befalling it and how it constructs its response.
2. IOTL, the Qing government believed that the cause of the economic issues was government corruption. This wasn't actually the case, but it was an interpretation the emperor and the court faction built up around him were predisposed to because of the corruption scandal with
Heshen and the inflation that had been going on since the 1790s.
When the opium issue became really prominent in the 1830s, the government seized on it as yet another reason for the problem, with Qing officials estimating that 50% of Qing yearly revenue was bleeding away due to opium smuggling, when in reality the figure was closer to 20% -- and of course, they completely failed to factor in the main reason for the economic crisis: no new silver coming in from Mexico. Because of this misinterpretation of events, the Qing government's response to the two crises was to further double down on its anti-corruption policies, which didn't work because it wasn't addressing the real reason for the economic crisis. In fact, the Qing economic crisis wouldn't end until Mexico finally stabilized and began exporting reliable silver dollars to China again in the 1840s.
In the decades leading up to the Opium War, there were government officials who were concerned about Britain's technological superiority, but the emperor's faction always responded to their concerns by saying that even if the British
were technologically superior (which the emperor finally
acknowledged in 1842), they could only be dealt with after the horrific corruption they believed was plaguing the government was rooted out first. In reality, there was a certain low level of corruption endemic to the Qing bureaucracy, but it was nowhere near as acute as the imperial court were convinced it was.
3. ITTL, the opium issue comes up in the late 1810s and early 1820s, before the economic crisis becomes a major concern for the Qing government. This means that instead of associating the opium issue with internal corruption, the Qing instead associate it with foreign encroachment on China and the need to catch up with the foreigners. If the Opium War starts a decade or two earlier than IOTL, the need to catch up with the British will take precedence, especially if a Second Opium War happens 14 years later, like IOTL, and reinforces that idea. This will, among other things, massively improve Qing performance against the revolts of the 1850s-70s that popped up IOTL.
And if the Thirteen Colonies staying in the British Empire results in the Spanish American colonies not rebelling in the 1810s-1820s, the Qing economic crisis will either be prevented or delayed by several decades, meaning that the different crises that came together in the early 19th century will be even more separated in time, allowing the Qing government to focus on one at a time and to start catching up with Europe early.