I only know about Johnston as far as the Vicksburg Campaign is concerned.
On May 13th, he landed and assumed command of the troops in and around Jackson. This included 4,000 combat ready troops, 2,000 men that had been fought to exhaustion at Raymond, and a smattering of state troops and local militia.
Was he too late, as he wired to Richmond? Too late to save Jackson for sure, even if we only count the army corps he knew about on the Clinton road.
He sent 3000 troops out to delay the corps at Clinton, 1000 troops to delay the troops south of the city, and posted the 2000 exhausted troops from Raymond north of the Clinton approach as a distraction. Then he set about extracting all of the supplies from the city and planning to retreat north. After the retreat, he ordered Pemberton to attack "Sherman" (actually McPherson) at Clinton, regrouped south of Canton, and began marching towards Livingston.
To my knowledge, there was no direct road from Livingston to Clinton at the time. For all purposes, I consider the order to attack Clinton a disguised order to abandon Vicksburg.
By the time Johnston reached Livingston, Pemberton was fighting Grant at Champion Hill. When Johnston received word of the defeat at Champion Hill, he turned his army around, marched back to the railroad, and reoccupied Jackson.
I'm on the fence with what Johnston could have done. One one hand, it took several weeks for Grant to complete the encirclement of Vicksburg. On the other, Johnston had no supply line to the city.
I lean towards Johnston placing Gregg in overall command of the troops retreating north of Jackson and riding from Jackson with Wirt Adams' cavalry to Edwards Station via Livingston and Brownsville. If he wanted to abandon Vicksburg, he should have stepped up and done it himself.