It can be an excellent safety, but it has to be fitted. Almost sounds to me like the safety lever is rubbing on the inside of the stock - maybe not actually moving its full distance. I am wondering how your action is set into that stock - seems to me I see "scratch mark" or wear mark just opposite your safety where the bolt shroud might be rubbing on the stock on left side of the tang - that would indicate that the action is too low in the stock. Also, the rear of your tang looks to be very tight - there should be a gap there - 1/32" or more. Best check is to get the entire metal parts out of that wood stock and re-assembled - then try the various functions. I am not sure that kind of safety has an audible "click", but mine have a very definite tactile click when the little ball pops into the hole - you will see all that once you get it apart. I have several bolt rifles with similar looking safety.
To reiterate what a previous poster wrote - I have a mauser, with a very heavy 26" barrel chambered in .243 Win, with a monster big heavy thumbhole stock. I built it to be a "shooting table and sandbags" gun - it has a single shot follower, so I can just drop a cartridge into the mag opening and close the mauser bolt - you can not single feed an original mauser any other way, except from the magazine. That rifle has no safety. Doesn't need one, for the use I built it for.
And, over the years, I have been known to "glue" things together by not being totally careful with the release agent, or not expecting the epoxy to flow where it actually went. And I have bought rifles on this site that had variations on that theme. Some minor, some not so minor; it happens.