Probably the easiest thing to try is a new recoil spring. Yes, a defective/worn recoil spring can be involved in failure-to-extract issues. I'd try a new factory spring and then shoot the same ammunition again.
If it were a M4006 brought to me, as an armorer, I'd inspect the extractor hook for chips/breakage, and check the extractor spring tension.
A weakened/too light extractor spring can cause failures-to-extract when the critical 'moment of mass' occurs as recoil forces travel throughout the gun. The front of the extractor wants to pivot outward (under recoil force), away from the case, and it's the job of the extractor spring to resist that force & movement. If the spring is too light, the extractor bounces out & away from the case rim at exactly the wrong moment, meaning it slips over the case rim, resulting in a failure-to-extract.
Armorers use a force dial gauge to check spring tension at the moment of extractor deflection (pulling on the extractor hook with a special hook attachment on the gauge, reading the tension at the moment the extractor starts to move). The normal range for a .40 (and 10mm) is 4-8lbs. Some guns may run better at one end or the other of the normal range, and yes, changing to a harder recoiling, much lighter bullet weight type of ammunition
may have an influence on this.
If you were to look back through the extractor springs recommended in the various 4006/4006TSW/411 models, there have been at least 4 extractor springs listed at various times, and I've seen 3 of those listed at one time or another as "standard", in different models & production vintages. What's been considered "standard", "revised" & "optional" has varied a bit over time. The "R4" extractor spring later used in the older M4006's is currently the standard "production" spring, but there are still a couple optional springs that are listed (which may be needed for an occasional gun).
For example, one of the new production 4006TSW's we received in the late/middle 2000's was exhibiting occasional failures-to-extract for a shooter (using 180gr duty loads). When it was brought to my attention, I checked the extractor spring and saw that it was under the 4lb minimum of the normal range. The extractor hook, barrel chamber and recoil spring appeared fine.
The extractor spring was the "standard" (unpainted) spring, (#100870000), which was the "R4" optional spring in the older 4006. Confused? It gets better.
Thinking the spring might be defective (it happens), I tried a new spring of the same part number. The tension was still below the recommended tension. Apparently, the spring well in the slide may have been at (or over) the deep end of the normal spec range. Fine. I tried a couple of the optional springs, finally getting a good tension within the recommended range when the "orange" spring (#238650000) was used, which is a heavier-than-standard spring for the .40 models. After seeing the bench checks within normal, I tried the gun downrange, and found normal functioning to be restored. No more failures-to-extract ... and feeding was also fine (too heavy of an extractor spring can cause feeding problems).
Now, doing trial & error without having a Wagner Force Dial gauge at your disposal ($150 tool), and knowing
how to use it to get an
accurate reading, even if you do have one, may be a frustrating experience.
Also, interestingly enough, I once learned from a much more senior armorer (whose agency used 4006's) that sometimes an extractor needed to be "tightly blocked" in some guns. That means the extractor bar block gauge might need to have the "GO" end fit more tightly than might be "normal" in some other guns. (1 too many file strokes on the adjustment pad of the extractor can throw that right out the window.) He helped me solve a problem in a very early 4006 back then.
Too much trivia and background info, probably.
Bottom line?
It might be the specific ammunition. If the gun isn't producing FTE's with 180gr loads, it might be the lighter bullet weight ammo is a bit hot (and the spring can't resist extractor deflection under the increased recoil forces), or, the ammo case rims might be on the small end of normal spec, or both. Or, the spring is starting to approach becoming worn out, and it may be the hotter ammo that's making it first noticeable? Who knows?
Normal factory recommendation for LE duty guns is to replace the recoil spring either every 5 years (of service, not sitting unissued in a box), or every 5,000 rounds fired, whichever occurs first. Try a new factory recoil spring.
If the extractor hook appears in good shape, and the new recoil spring doesn't work? Then it's time for someone to check the tension, meaning preferably someone with the right tool and some knowledge of S&W pistols, and who has some different factory springs they can use to try to restore the recommended tension range in that particular gun.
Just my thoughts. I obviously can't know what's happening in your gun unless I could examine it and try it, and preferably watch you shooting it, with different ammo, and when the FTE's happened.