I have been wondering exactly what the perception of them in the UK is. I would have guessed that it is what you said. It is very clear they tried to manipulate the situation to their own advantage and disrespected the Queen in the process. I wonder if someday Harry will regret all this.
We can't know if we don't know Harry personally. I suspect that the Sussexes have been through a great deal of emotional and logistical upheaval during the first years of their marriage, along with the demanding yet happy and fulfilling responsibilities of parenthood. Plus, all of this came after a deeply meaningful romance and courtship of a year-and-a-half that they consistently kept under-the-radar. It's to the Sussexes' credit that their union has only seemed to grow stronger and deeper amidst all of the outside sturm und drang that has surrounded them.
To paraphrase Camilla's famous comment after the Sussexes' engagement, I recently heard this said about the Sussexes' departure from senior royal service:
"The U.K.'s loss is America's gain (or re-gain in Meghan's case)." 
It's been reported that Harry remains close to his father and to the Queen. Probably, once the pandemic has run its course, the Sussexes will make some trips to the U.K. for family-related events on occasion, and to continue assisting their patronages. They haven't abandoned any of their patronages. As with most of the world, activities, events and business matters are routinely being conducted via online technologies these days. And we are not privy to everything the Sussexes are doing on a daily basis with their current and future goal-oriented endeavors.
But he wasn’t named president by the board he was given that role by the queen. And I’ve seen this theory that it was Harry’s gift to the queen only from the Sussex fans I have not seen a legit source to confirm it.
I'm not sure what your last sentence means exactly. The QCT is not Harry's gift to the Queen. It might be
her gift to Harry, but not the other way around.
It doesn't matter if Harry was named to the Presidency of QCT by the Queen. Her Majesty has no direct, day-to-day input or control over the QCT, despite the fact that the organization was created at her behest. The same goes for Sir Christopher Geidt, who was named by the Queen to a direct, full-time managerial role with the organization after he was forced out of his position as the Queen's private secretary (by Andrew's and Charles' courtiers). If the QCT Board wishes to fire and replace Sir Christopher, they could. I doubt there is any reason for that to happen though.
Similarly, I do not see the Board at this juncture, deciding to strip M&H of their substantive roles with the organization. Remember that we do not know anything about the work that the Sussexes are doing behind-the-scenes with the QCT and with their U.K. patronages. What we
have been given is a glimpse via two QCT videos, of M&H in conversation with young QCT members around the world.
Meghan & Harry are a busy couple, that's for sure. In view of the pandemic and their house hunting search and eventual purchase, they have certainly been accomplishing a great deal, and not slowing down in the least in terms of their projects. Still, it must be great for them to be able to spend so much core family time together during this 'stay-at-home' phase that's going on worldwide.
For those wishing to discuss the FF book, there's a separate thread available.
