So for the "why do people think DeSantis is doing a good job on Covid" question. Here's a comparison of Florida to 3 other states that went with very strict lockdowns and mandates on the following dimensions: 1) per capita death (per million), 2) % population over 65 (79% of Covid deaths occur in this age group), 3) unemployment rate (proxy for economic situation in the state and 4) vaccination rate (% fully vaccinated).
Florida: 1) 1808, 2) 20.5, 3) 5.0, 4) 48.6
New York: 1) 2787, 2) 16.4, 3) 7.7, 4) 56.8
California: 1) 1628, 2) 14.3, 3) 7.7, 4) 52.5
Michigan: 1) 2119, 2) 17.2, 3) 5.0, 4) 48.7
So despite having a higher proportion of at risk population Florida fared considerably better than New York and Michigan in Covid deaths per capita. California did better but has a relatively younger population. For reference, Florida ranks #2 in population over 65, California ranks #45. Second for reference, Florida ranks at about 25th for Covid deaths per captia; California is slightly better at about 18th. New York is #49 and Michigan is #12
Florida is below the national average in unemployment while the restrictive states of New York and California are considerably above the national average. Michigan is fairing the same as Florida.
So I'd guess the praise for DeSantis is that his limited restrictions do not appear to have been more dangerous for the population than those in restrictive states that either had worse (much worse in the case of NY) Covid outcomes and/or more severe economic consequences.
There are likely governors who had better outcomes but DeSantis showed that you don't have to lock down everything and exercise massive executive authority to have good outcomes.