We can look at an example of a more detailed gift roll from John Nichols "The Progresses and Public Processions of Queen Elizabeth: Among which are Interspersed Other Solemnities, Public Expenditures, and Remarkable Events During the Reign of that Illustrious Princess, Volume 3”. It's an old source but includes transcriptions of primary source text. There are generic gifts of coin or gold plate (the crown kept up a steady supply of gold plate for these occasions so everyone who did not receive a personalised gift could receive these instead to sell for money). But there are also more specific gifts mentioned. One example is from Lord Hunsdon the Lord Chamberlain, an intimate and relative of the Queen, of "the nether skirts of the coveringe of a gowne, black sticht cloth, florished with gold, with some owes". "Owes" are according to Janet Arnold's "Queen Elizabeth's Wardrobe Unlock'd" (1988, 2020 ebook edition) circular gold or silver spangles, ie metallic sequins that might resemble the letter O. So this is a decorative layer for a skirt in what is probably black silk, with gold patterning and spangles. We also see in this gift roll collars, chains, fans, safeguards (outer protective skirts for outdoors), a porringer (soup bowl), a stool, and a decorated box for sweets (a comfit box which holds pieces of candied fruit). Hunsdon's wife gave the Queen a matching "pair of bodies" (a form of bodice) to go with her husband's gift. So people certainly gave gifts that were both expensive and personal. There was a certain amount of work and symbolism that went into them.

A large amount of correspondence around what to get between family members and receiving advice from friends can be seen in Arnold's book. Also featured in “Rainbow for a Reign: The Colours of a Queen’s Wardrobe” by Jane A. Lawson (2007) which also delves a bit into the symbolism (particularly of colour obviously). Maria Hayward's Gift Giving at the Court of Henry VIII:
The 1539 New Year's Gift Roll in Context (2005) mentions aspiring authors giving gifts of books they wrote hoping to receive royal endorsement or patronage. As covered by Arnold's book, it was quite common from royals, aristocrats and gentry to give away at some later time items of clothing to their attendants if they did not want them or were done with them. Monarchs in particular received so many gifts of clothing that that they had plenty to spare. So not everything was actually worn by the monarchs. Furthermore, the wardrobe at the time was not a cupboard or closet, although closets for that use also occurred at this time, the Royal Wardrobe was a whole large building which hold most of the royal garments except for the select few that were actually stored in a closet with the monarch (see
“Tales From the Royal Wardrobe”, Lucy Worsley (2014) https://www.youtube.com/watch?v=DZDvS2o5Pdw sorry that this recording is a little dark).
So many of them could lie in the wardrobe collection for months or years in between uses, being specifically called for during the time they were wanted as described in "The wardrobe goods of Anna of Denmark, queen consort of Scotland and England (1574–1619)"by Jemma Field (2017), which is a good work to read if you are interested in detailed fashion history. It was therefore not entirely surprisingly if they did not wear them, or took a certain time to get to them, and it was considered an encouraging sign if the monarch was seen wearing (or using in the case of other items) the gift someone gave them within a short time of receiving it. If a month later the monarch is see wearing your item it is probably an intentional choice signifying approval, and they would certainly be less likely to do so if you are out of favour. "Rainbow for a Reign" ends with a message from Elizabeth Wolley in 1592 to her father saying "yesterday she wore the gown you gave her". But giving a poorly-received gift doesn't really seem to have been a prelude to any deaths. It might signify other forms of dissatisfaction, may even be entirely for other reasons that they don't use it, but it doesn't seem to have been take quite that seriously. And I'm not aware of any instances of the monarch refusing to accept a gift altogether. If they were to do that I suspect you would just not be invited at all.

In a similar way to those received, the choice of specific items at Christmas or New Year given by the monarch was also considered and often symbolic. Many of the more specific items were also made by the royal goldsmiths who made gilt silver plate, with items like "a pair of gilt great pots" (Heyward). But in 1533-4 Anne Boleyn gave her ladies palfreys (horses) and saddles (possibly symbolic of their role as attendants because they would have accompanied her when she went riding, and horse-riding was symbolic of their status as gentlewomen). Heyward also records Henry giving beads of jet to some of his lower staff (pages and cooks). Heyward notes that your suspicion is correct that the monarch generally gave less in value than they received. Sometimes to save money during tighter years old unwanted gifts were repurposed for a different New Year as gifts from the monarch. Which feels slightly cheap of them, but then as I said before they received so many gifts that they had plenty to spare.