“New standard bearings on the way...”
To make extra sure, look at the back of the old bearing shells for “STD” to confirm. Unless the engine was previously rebuilt and needed the crankshaft reground, STD is what should be there, Otherwise, it would be .010, .020 and in less common rebuilds, 030 and .040.
However, the lower ends usually hold up very well. I recently took a 4.6 crankshaft to the machine shop to have it checked. It was still well within standard spec with over 100,000 miles and removed from a very poorly maintained engine (loaded with sludge). I had them polish the journals and that is all. The connecting rods were all in perfect shape as well.
Tapping is usually lifters (and related valve train noise) and sometimes slipped liners. Slipped liners are extremely uncommon on a 4.0 and almost unheard of in earlier versions, such as a 3.5. It is much more common in a 4.6. Most Rover V8s - 3.5, 3.9, 4.0, 4.2, and 4.6 almost always develop lifter tapping when they get miles on them. My TR8 with a 30,000 mile 3.5 has moderate tapping. It is a common trait of all engines of that basic design, including the GM 215 V8 and all similar variants including the Rover V8. Im not the least bit worried about my TR8 as oil pressure is great and it runs fantastic. I also have a 96 D1 with a 27,000 mile engine that if I really try hard to hear, there is a very faint lifter tap starting to develop. I have another 96 D1 with 130,000 miles on the engine that has just a bit louder tapping but also quite mild. Alternatively, I have a recently rebuilt (previous owner) 4.6 that I cannot hear any tapping at all but has the lowest oil pressure of all of them. I suspect the oil pump casing is well worn.
Again, lower ends generally hold up very well (aside from slipped liners on some, mostly 4.6s). I would say most of us just live with the tapping. A new cam, lifters, and valve job / resurface often is all that is needed to make it go away and restore lost performance. Camshafts due tend to wear well in advance of the rest of the engine. More than likely if you had a rod tapping you would also have poor oil pressure.
In my opinion, some shops will blame the lower end for tapping noises and then not want to do the repair because just changing rod bearings often doesn’t solve the problem and is an indicator the rest of the engine is on its last legs. No shop wants to charge hundreds (at least) of dollars and give you back a vehicle that isn’t really repaired and could cause angst with the customer.
Some will argue that when you have lifter tapping it really needs to be addressed. However, I have never taken one apart specifically to address that and never had a negative consequence such as a lifter completely failing or cause other problems than noise.