Perform a Nested Permanova in r

Question

[Mgs3]

I'm studying the effect of three conditions on the microbial distribution in the rhizosphere of grapevine plant. I have three conditions:

Type of soil: Manure, Peat, Sand

Soil sterilized before planting: Yes, No

Root sterilized before planting: Yes, No

I was suggested to use a nested permanova, so that root sterilized is nested in soil sterilized which is nested in type of soil. Basically to see if within the type of soil the soil sterilization had an effect, and if within the soil sterilization the root sterilization had an effect. First question is if the script below is correct, and second if you think the analysis is appropriate. I'm also trying to discover is there is an appropriate way to perform a pairwise test

adonis2(vegdist(tOTU_sed, distance="bray")~Soil / Ster_soil / Ster_root, permutations=1000, data = META_sed)

Permutation test for adonis under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 1000

adonis2(formula = vegdist(tOTU_sed, distance = "bray") ~ Soil/Ster_soil/Ster_root, data = META_sed, permutations = 1000)
                         Df SumOfSqs      R2       F   Pr(>F)    
Soil                      2   3.7770 0.43698 16.2502 0.000999 ***
Soil:Ster_soil            3   1.0810 0.12506  3.1005 0.001998 ** 
Soil:Ster_soil:Ster_root  6   0.9964 0.11527  1.4289 0.022977 *  
Residual                 24   2.7891 0.32269                     
Total                    35   8.6435 1.00000                     
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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1