LONDON — Shortly before 8 p.m. on Friday, King Charles III took up his post at one end of the catafalque in Westminster Hall, standing a last vigil over the coffin of his mother, Queen Elizabeth II, along with his sister and brothers.

It was a deeply personal moment, but like so many during the king’s hectic first week on the throne, one bathed in the glare of television cameras. Many of those moments have been majestic and poignant, not least in Cardiff, where Charles, who until last week was the Prince of Wales, traveled on Friday.

The king shook hands and took flowers from children, an echo of last week at Buckingham Palace, where a woman in the crowd kissed him. He addressed the Welsh Senate in Welsh, speaking of his love “for this corner of earth.” He laughed softly as he chatted with well-wishers, looking refreshed after a day out of public view Thursday at his country house in Gloucestershire.

Yet there have been a couple of other moments — both involving uncooperative fountain pens, as it happens — that revealed a less poised sovereign. In one, he impatiently gestured for aides to move an inkwell and tray of pens out of his way. In another, he sputtered, “Oh God, I hate this!” after a pen leaked on his fingers.

To some, those episodes were an unflattering window into Britain’s new king, suggesting peevishness and a sense of entitlement. To others, they simply caught a 73-year-old man, harried, grieving and under strain, reacting to the kind of mundane mishap that plagues ordinary people every day.

“We must remember that unlike his mother, the new king was born to be a future monarch,” said Paddy Harverson, who served as communications secretary to Charles from 2004 to 2013.

“He brings all the positive and negative elements of his experience — and the way those experiences have made him the man he is today — to his new role as monarch,” Mr. Harverson said. “That includes the positives, like his informality in allowing the woman in the crowd to kiss him, and the negatives, like the impatience with leaky ink pens.”

For Charles, it also illustrates how, even after a seven-decade apprenticeship, starting a new job can be hard. That is especially true if, in the first week, it requires one to lead a nation in mourning a beloved queen while at the same ensuring the crown’s continuity by soldiering through a gantlet of signing ceremonies and other rituals that formalize the transfer from one monarch to another.

“Think about it,” said Geordie Greig, who edited The Daily Mail and Tatler magazine. “Your mum’s died, you lost your job, you’ve got a new job, there are disputes in your family, and the world’s cameras are on you.”

“However well you’re prepared,” Mr. Greig said, “there comes that moment when you have to jump in the pool.”

By any yardstick, the king has gotten an enthusiastic reception. Public support for him has soared in the first few days of his reign: 73 percent of those surveyed by the public opinion firm YouGov said Charles had performed well, while only 5 percent said he performed poorly. Sixty-three percent said they expected him to be a good king, compared to 39 percent who said it in a poll last March.

How long that honeymoon will last is another question. Charles will be crowned, likely next spring or summer, which will draw the country into another round of pageantry. But between now and then, Britons will go back to their normal lives, faced with a spiraling cost-of-living crisis, labor unrest and a likely recession.

The king appears sensitive to those issues. Reports emerged this week that Buckingham Palace is planning a relatively restrained coronation ceremony. He has led a longstanding effort to streamline the royal family, in part to shield it from complaints that it places too great a burden on the public purse.

Still, Charles faces a more personal challenge. While the monarchy is in no imminent danger of losing public support — indeed, the outpouring of love for Elizabeth may temporarily deepen support for it — replacing the queen will be hard. Dignified, stoic and unwavering, she rarely put a foot wrong in public. Her views on most issues were a mystery, which kept her at a strict remove from politics.

The king, by contrast, has passionate interests and strong views, on issues ranging from climate change and organic farming to architecture. As a prince, he could voice those opinions, even if he generally did so in diplomatic language. Now, as he acknowledged last week, he will have to stifle himself.

On Friday, the king signaled his continuing commitment to religious diversity in Britain, which has long been one of his concerns. Speaking to religious leaders at Buckingham Palace, he said it was a duty of the sovereign “to protect the diversity of our country, including by protecting the space for faith itself.”

But other issues could prove more problematic. On his visit to Belfast earlier this week, the king raised eyebrows among political analysts when he met Michelle O’Neill, the leader of Sinn Fein, the Irish nationalist party, which became the largest party in Northern Ireland in elections last May.

Taking note of the victory, Charles praised Ms. O’Neill for her party’s “skill and ingenuity.” He then turned to Jeffrey M. Donaldson, the leader of the Democratic Unionist Party, which had been dethroned by Sinn Fein, and said, “I have seen you occasionally,” before turning back to look at Ms. O’Neill and adding, “in the past.”

The king, people who worked for him say, reads widely and is copiously briefed before his meetings. Yet his interests, such as agriculture, have a way of coming through. Last April, he visited a British aid organization, World Jewish Relief, that is sending food and medicine to Ukraine and helping people escape the war.

Charles listened politely as Katya Newman described how the group, of which Charles is a patron, had helped her mother, Larysa Roshchyna, and her 90-year-old grandmother, Kateryna Razumenko, get out of Kharkiv, the eastern Ukrainian city that had come under relentless Russian bombardment.

“So, what do you think the aim of the Russians is?” Charles asked the three women. “Is it to remove people?”

Then he steered the conversation to Ukraine’s inability to ship its grain because of Russian blockades. Charles questioned whether outside powers could work with Ukraine to find alternative routes to transport its harvest. “You do the same with refugees,” Charles said. “Couldn’t you do it with grain?”

His hosts looked puzzled. But, as with his early interest in the environment, which prefigured climate change, Charles was on to something. Three months later, Russia and Ukraine, along with Turkey and the United Nations, brokered a deal that allowed ships laden with grain to sail from Odesa and other ports.

During that visit, as in so many others, Charles was unfailingly polite. But the incident with the pens showed another side of him: a royal who is used to having people at his beck and call. And unlike the queen, who showed preternatural discipline in public, the king is prone to the occasional outburst, royal experts said.

“It’s quite a cosseted life he’s lived,” said Edward Owens, a historian who has written about the royal family. “Charles has been waiting for this moment for a long time. But he’s existed as someone who hasn’t had his opinions challenged enough.”