What are 'SWEETS' called in British English? (food with a lot of sugar in it - ice cream, cakes, pies, percy pigs etc.)?

"sweets" usually refers to pieces of candy, but you might hear "a sweet" used to refer to a dessert after a meal (e.g., "do you want to get a sweet?")

There isn’t a term that combines sweets, ice cream, cake and pies under one. Sweets is the equivalent of candy but does not include chocolate bars

Most commonly, dessert (when at the end of a meal). Some people say pudding, but that's more colloquial / less formal. Outside the context of a restaurant, we wouldn't usually use a collective term for the things you've listed. An ice cream is an ice cream, a cake is a cake, mince pies are mince pies, etc. Percy pigs are sweets (or sometimes sweeties).

Sweets also isn’t as common in the US (or where I live specifically therein) as you think. I don’t know anyone my age or younger who says it. (I only bring up American English because the phrasing of the post implies the comparison.)

In American English we use "sweets" to refer to any sugary sweet foods: candy, ice cream, cake, cookies, etc. In British English "sweets" refers to just candy. I don't think they have a word for "all sweet sugary foods" but maybe a Brit can correct me on that if there is.

I think the closest umbrella term you could get is pudding. Pudding being the (usually) sweet treats after the evening meal but I'd never call a percy pig a pudding, only bigger things

Basically equivalent to candy

I wanted to comment on your use of "I feel like.". It is not an intuitive, subjective or personal matter what things are called. You should say "I think that "sweets" are such-and-such. You can say " I feel like going to the movies." "She feels like breaking up with her boyfriend."." Do you feel like quitting your job?" "Feel like" is used to express your personal whim.