Howdy
I did a photo comparison of a S&W Model 17 and a Model 617 a few years ago.
Here are a few photos that may prove interesting.
This first photo is of a traditional forged and machined thumpiece on the left, and a MIM thumbpiece on the right. NOTE: this is not meant as a condemnation of MIM parts, I just wanted to compare the two technologies. If the OP's Model 629 is very new, I have to assume it is mostly made with MIM parts. I will also assume that although the 22 caliber parts I am showing may not be identical to what is in a 629, I'll bet they are pretty close.
Interesting to note that the slotted part that fastens the thumpiece to the underlying cylinder bolt is a nut, not a screw. It looks like a screw because it has a slot to tighten or loosen it, but it is actually a nut.
Now look down in the hole in the MIM part where the nut rests. Notice those spiral marks cast in? I don't know this for sure, but I believe they are there to act similar to a locking nut, Helping to hold the nut in place without it backing out.
Here are the undersides of the two parts. Those machining marks around the forged part are simply tool marks left behind as the part was machined. The underside of the MIM part is a bit more complex. The four slots at right angles are positioning features that help line it up properly when assembled to the underlying cylinder bolt.
Here are the cylinder bolts the thumpieces fasten to. These are the parts that slide forward when the thumpiece is slid forward, the rod shaped part at the top presses the back of the extractor rod forward, freeing the cylinder to swing out. In this case the MIM part is on the left, the traditional fabricated part is on the right. Notice the shape of the threads on the MIM part. These are the threads that are engaged by the nut when it is torqued down to hold the thumpiece in place. The MIM threads are interrupted. They do not go completely around the feature the way the threads do on the fabricated part. If you look carefully at the MIM part you can see the parting line where the 'green' part was formed in a mold. To remove the part from the mold, I believe it was simpler to interrupt the threads so there was a flat surface that could be popped out of the mold more easily. Bottom line, less thread contact with the MIM parts than with the machined parts.
Does this really matter? I don't know. I have dozens and dozens of Smith and Wesson revolvers from every era starting in the 1850s. I have never had a thumbpiece pop off. I don't think I have even ever had one come loose. Granted, my only 44 Mag S&W is a Model 29-2 that left the factory around 1967. I have not put enough rounds through it to shake anything loose. I seldom fire it with anything other than 44 Special loads.
So, blue loctite is probably a good idea. Clean the threads thoroughly with solvent to remove any grease or oil. Both the male and female threads. I wish I had a figure to give you for how much torque to use to fasten it in place, but I don't.