In his three volume History of the Vicksburg Campaign Ed Bearss covers Johnston's movements & dilemmas. There is no mystery about what Johnston was up to. It is all thoroughly documented.
When Grant crossed the Mississippi River, he was greatly outnumbered by CSA forces in Mississippi. Bearss goes into great detail documenting the masterful way Grant used cavalry & the threat of landings from the river to keep CSA commanders completely wrong footed. Constant feints toward the vital rail road kept Pemberton's cavalry chasing ghosts. Not only did Grant's cavalry campaign keep their much larger opponents off balance, it kept them both occupied & unable to make mischief.
Johnston suffered from the same problem as all Grant's other opponents did. He had no idea what Grant was going to do next. Even Sherman stated explicitly that he had no confidence that the unsupported move against Vicksburg would work until it did. Grant's operations were classic examples of the OODA Circle. By the time Johnston & Pemberton realized what Grant was up to, he was already several moves into his next phase.
Both Johnston & Grant understood that it was Pemberton's Army, not Vicksburg that was the key to victory. With Pemberton's Army intact, Johnston had options; Vicksburg could have been retaken. As events unfolded, Johnston ordering Pemberton to abandon Vicksburg was the correct decision. Pemberton chose, instead, to follow Davis' meddling order to hold at all costs.
Once Pemberton ordered his army to man the Vicksburg defense & Grant reached the Mississippi upriver, it was only a matter of time. With Grant's riverine supply line absolutely secure & nowhere for him to draw a relieving force from, Johnston's options were extremely limited.
On July 4th, not only was Vicksburg secured, but the Tullahoma Campaign had swept the Army of Tennessee clear out of the state & permanently lost the all important initiative in VA. By late fall, Bragg would be in North Georgia & Grant's line would run from New Orleans to Cumberland Gap. Johnston's Army of relief seems a mere trifle compared to that, ¿no?
Note: in his letter to Davis laying out his plan for the Pennsylvania incursion, Lee asked Davis to concentrate 100,000 idle troops from the Carolinas under Beauregard at Culpepper VA.
While Lee's Carolina 100,000 twiddled their thumbs amongst the palmettos, by July 4th Lee, Bragg & Pemberton had been soundly defeated. The initiative in VA & strategically vital Vicksburg & Middle Tennessee were irretrievably lost. The responsibility for that colossal defeat does not lie with Johnston.