It appears ...Chad and JH... have answered most of your questions regarding what folks call your Chiefs Special. I will continue to call it a .38 Chiefs Special with a five-screw frame.
My database lists many serial numbers Messrs. Supica and Nahas did not have access to for those early editions of their fine tome.
The five-screw carbon steel Chiefs Special serial range is 1 - almost 46000. In that range I've estimated about 6,000 numbers are aluminum alloy Chiefs Special Airweights.
Smith & Wesson neither produced nor shipped Chiefs in serial order so you must be skeptical about serial and date ranges. The sole way to know the exact day yours departed the plant is to obtain a letter.
The serial number spread shipped in 1950 includes 6 - X59, 1951 includes serials 1 - 1825. Carbon steel serial numbers shipped in 1952 span 132 - 24825, and a number of Chiefs Special Airweights shipped in 1952 also.
Ah, the thumbpieces. You're looking at long out-of-date details in the older copies of the Catalog. One of my displays at the June 2025 Smith & Wesson Collectors Association symposium in Concord, North Carolina, portrayed thumbpieces the company used on Chiefs Specials from 1950 - 2025. I showed seven variations of the flat thumbpiece in my display. The first one had a short lifespan, and we had only seen it on serial numbers 16, 34, 99, and 101 (1950/51). History can change quickly. I saw serial number 54 in Concord, and it has the first flat thumbpiece. This month I've now seen serial numbers 10 and X58 (the second and third Chiefs Specials to ship in December 1950), and they also have the first flat thumbpiece. A gambling man might wager there are more.
Known second flat thumbpieces--like your plump oval thumbpiece--span serial numbers 111 - 36722 (1951/53).