one solution i was going to suggest was if it wasnt too many boards that had large gaps, was to install some very short pieces of floor to bridge that gap, which is still an option, just a matter of time and patience on your end. building out the base and shoe mouldings will achieve the same result.

I doubt very much that these gaps are the source of bugs...there are too many other ways they can get in. Using bug spray monthly inside your home is unwise from a health risk standpoint: that practice is potentially more injurious than anything the bugs could do. However, if you want to deal with those minor gaps, white painters caulk applied by someone with caulking experience will make them disappear. If you don't have experience caulking, enlist someone who does. It would be very easy to caulk that well and neatly if you know what you are doing, and very easy to have a mess on your hands if you don't.

Politely pose your question to the builder, and check the amount of bearing there is where the end (both ends) of the floor trusses rest on the walls. Even if you get a BS answer, you have brought it to the attention of the builder. Years ago I had a project where there was two doors leading from the garage into the house in a non-bearing wall. During the rough framing I noticed one door's header was immediately above the door opening and the other door's header was about a foot higher immediately below the garage ceiling; both door openings were the same size. When I asked the builder why the difference, he started explaining about the earth's rotation and the westerly winds and the moon's position and the wood species and the moisture content and snow loads and . . . I stopped him and asked, "It's just because its the way it happened, isn't it?" He replied, "Yes".

If you install stringer skirting it will take care of the gap as it seems it was removed to install the carpeting. It's usually a 1/2" or 3'/4" thick wood along the wall with an edge molding. Here are some pics and a site. https://knostairs.com/wp-content/uploads/2020/01/Skirting-molding-up-flight.jpg You also should install cove/edge molding under the tread (see below). If you want something simple for a molding, there are several you can choose. These details will make your stair look finished with nice details. "a" is the tread. "b" is the cove/edge molding.