Well, i can't imagine circumstances, where Democrats (especially - with present left-leaning (despite some remnants of conservatism on such issues as choice) party in very socially conservative state) would hold governorship in 2023. Yes, Louisiana elects probably the most conservative Democratic state legislator in nation (IMHO, that's Francis Thompson, but he is a product of another era), but JBE was so much an exception (generally socially conservative populist with extremely damaged opponent) in 2015, that it would be naive to think it will happen again soon. So i would even consider "the least objectionable Republican" (of Dardenne-type for example) as reasonable alternative. We shall see whether it will become a reality..
And Edwards narrowly won reelection in 2019 against an opponent who was not that impressive and was a staunch Trumpist. Thus, I agree with you that it is highly unlikely Democrats hold the Governorship in 2023. If a popular moderate Democrat can only win by a few percentage points, a Generic D would easily get blown out by double digits.
Yeah, it's quite hard to imagine Ds holding here. If Rs pull out a Bevin type, Ds might win in 2027. But this is the tough hold to make all tough holds look tough.
I personally rate it Likely R, much closer to Safe than Lean.