How extensive is this home repair?

get a plumber and $5000 .. to fix it ..

no don't replace that there is no need 

We can't tell you what the extent of the damage is, but a contractor can. You will most likely need to have the entire thing ripped out and examined carefully--treated wood doesn't mean it can't be damaged.  

The extent of long term water damage CAN'T be estimated without SEEING the structure. Even a professional ON SITE may not be able to determine the full extent until they actually start tearing apart the visible damage.

Chris: The actual plumbing will be the SMALLEST issue if it has been leaking for years.

Rip away any drywall with mold, get a plumber to fix the leak issue (that will be your biggest issue).

2x4s should be bleached if mold is present, but don't start cutting away at the house.

Let them air dry before covering them.

Polybutylene pipes "I believe" caused a ton of issues a LONG time ago at the connection points, there was a HUGE lawsuit and in many states, you can have them replaced, but I'm a bit ignorant of the matter.

Hopefully it's a simple fix and then just replacing the wall and flooring.

NOT CHEAP, but DYI will save you.

Square footage is "Length x Width" for carpet.

You want tack strips for carpet.

Thank God I RENT, hahaha.

Nope, not necessary.  Plumbers make sure it does not leak no where when they do their job.  However, you are talking about behind the taps, taps do wear out, so even a drip that only happens when you run water is a lot of water that just sits on the 2x4 and the rug and no air blows over it to dry it out so it has to evaporate.  If you have more than one person in the house then that tap is used more than just for YOU.

. still, wood is naturally resilient to water...which is why logs can float for years 10+ and not get waterlogged.

.  Carpets get shampooed and peed on by the dog, cat or rat.  What is behind the wall you never see...there is no carpet there, so the carpet is in the hallway or room so there is airflow that dries it out.

.  The wall wood NORMALLY IS NOT TREATED.  But it is fine.  Drywall (gypsum board aka chalk board) suffers the most.  So at most, after you fix the plumbing you put up some new gypsum board up to the faucet...and fit it in like a piece of a puzzle.  Screwing in behind the tub lower down is not necessary as you have to pull out the tub to gain access.

. Getting the old board out will be difficult because it is fastened to the wall BEFORE THE TUB WAS INSTALLED. so there are screws or nails on the lower part of the wall behind the tub.  You must clean the wall studs from the old screws(good thing they snap when bent) or use a long flat bar to bend over the nails so the wall is relatively flat.  Then you can insert you new gypsum board in and nail or screw the upper portion. The lower portion behind the tub does not NEED TO BE SCREWED INTO THE STUD WALL.  It can just sit there on the floor as the tub protects it...and holds it in place.

.  It is a bit fiddly but CAN BE DONE.  It does not need to be the blue drywall(water resistant) if you also have ceramic wall tiles...as the tiles are the waterproof barrier. So you got to do this part right.  Paint does not cut it.  Check out HOMO DEPOT or some other building supply store and see how they do their DISPLAY BATHROOMS.  There is a reason for the extra protection.  If all you had was paint and no silicone seal & grout then the spashing in the bathtub is the water that got in behind the wall...not a leak in the plumbing.   I have seen bathrooms where the walls were unpainted Plaster(which dissolves when exposed to water or molds up)

40+yrs in construction industry.

decide that after you remove the ruined drywall and can see what you're dealing with.  -- grampa

If it's been soaking for 4 years I'd replace it.  Just incase of mold ect.  I'd remove anything that was wet from the leak.

i would just hire someone that does that

i would talk to someone that does that