I’m a history teacher in Australia. I’m also a dual Australian/British citizen, an Anglophile, and a monarchist. I’ll try and give you what I would see as the general British - more specifically English - view of George III.
The most significant fact taught about George III in Britain, and the thing most people would know about him, is that he was mad. In modern day terms, he was mentally ill, and that has an impact on almost all thinking about him. His failures are often attributed to his ‘madness’ even in cases where there is little reason to consider that the case.
The length of his reign (1760-1820) means that from the British perspective, a lot of the view of him depends on what part of his reign you look at. Most regard him as something of a failure at the time of the American War of Independence - and have some sympathy for the idea that that part of his reign was tyrannical (I’ll come back to that in a moment though). On the other hand, during the Napoleonic Wars, he was a significant figure of national unity.
Overall, the view of George III in Britain is reasonably positive - losing the American colonies is seen as a failure, but that was a brief period in his overall reign. Was he a tyrant? From a British perspective, it’s hard to argue that. He basically let Parliament do what it wanted when it came to the American colonies - and he was supposed to let Parliament do what it wanted. The King of the 18th century did have more power and influence than the monarch does today - but the shift towards Parliament being more powerful than the King had already begun. You can argue that the War of Independence was serious enough that the King could have intervened more than he did - but he was supposed to intervene only in extreme circumstances. From the British perspective, rather than being a tyrant over the War of Independence, it’s more accurate to say that any criticism is that the King wasn’t tyrannical enough - he didn’t act to overrule Lord North even when it was clear that North was failing, even when the colonies made representations asking for his help in asserting the rights of British subjects he was supposed to guarantee. He followed the constitutional conventions of his day - even when a crisis might have justified him being more interventionist.
But overall, he’s seen as a decent King - he may have failed on that occasion, but he succeeded far more than he failed. And compared to his son (who became Prince Regent in 1811 and King George IV in 1820) he was seen as restrained and careful. He lost Britain’s first empire - but kept in intact during the Napoleonic period and laid the groundwork for its second greater empire.
A good summary but I would suggest you left out one of his biggest failures, Ireland.
Following the 1798 rebellion there was perhaps the greatest chance in history for Great Britain and Ireland to be reconciled for a fresh start and to allow Ireland to become a happy partner in the British Union in the same way that Scotland had become.
The disaster of 1798 in the middle of the Napoleonic war showed how shockingly badly Ireland was being governed. A small cabal of reactionary protestant bigots in Dublin controlled with an iron fist a desperately poor and oppressed majority-Catholic Irish population (no I am not a whingeing Irishman with a chip on my shoulder, these are simple historical facts). It was a time for London to march in and clean house and it almost did so.
Pushing through the Act of Union was achieved through bribing the Irish House of Commons (as well as being bigoted know-nothings they were also extremely corrupt) and at this point Ireland could have been admitted to the newly created United Kingdom as a sister nation with dignity and equality.
The Irish Catholic church was completely behind the Union as they recognised they could get a fairer deal from London than the bigoted minority in Dublin (it is one of the great ironies of history that the Catholic church supported Union while the Orange Order, the now loudest proclaimers of their Unionist loyalty, opposed it). Irish Liberals (in the old proper sense of the word) of all stripes also recognised the time for change had come, and even some of the protestant gentry, scared sh!tless by how close they had come to being massacred in the rebellion came around to Union, it was the last golden opportunity to put right the terrible wrongs that Ireland had suffered under British rule and start again with a clean slate.
George III blew it.
A simple, literal-minded man, with much sympathy with the backwoodsmen of the Irish ruling class rather than the sensible advice of William Pitt, he could not accept the right of Catholics to be elected to the House of Commons, thereby disenfranchising the vast majority of the Irish people. Ireland came into the Union as a second-class partner, her wrongs were not to righted, her people would not be equal, the resentment against British rule would bubble and simmer on after all.
The Act of Union failed, it failed because of George III. And I suggest that was a much greater failure than losing the American colonies, which was after all ultimately to Britain’s great benefit.