Have a look at something like this, there is a lot of these Indian wooden magnetic sets, it fits your criteria (just find one with notation): https://www.amazon.co.uk/Rusticity-Wooden-Foldable-Magnetic-Handmade/dp/B06WRNRH28/ref=sr_1_9?crid=3IWHZYDGJXIFS&keywords=Handmade+Wooden+Foldable+Magnetic+Chess&qid=1703123586&s=kids&sprefix=handmade+wooden+foldable+magnetic+chess%2Ctoys%2C96&sr=1-9
However I'd recommend you 12 inch set, 7"(18cm) is too small, and pieces for 12" set are bigger, better carved and better proportioned to the board. I use 12" for analysis.
I'm looking for a chess set that meets the following criteria:
I feel like I have gone over the entire internet looking for a chess set like this and can't find one. Lots of cheap wooden folding chess sets that are almost there but don't have the algebraic notation. If I weren't constantly out of money it'd be easier but I am broke all the time.
I mainly want it for looking at positions etc when I'm studying or doing puzzles.