In theory your results highlight a relative "large" separation (as far as the R coefficient is mentioned in other articles). The R coefficient in this case tells something about the separation. Considering bluntly stating that 0 means no dissimilarity and 1 strong dissimilarity. To draw a coarse analogy you also mention the correlation between y~x and indicate Rsq = 0.2 and p < .001. A nice NMDS biplot with colours or shapes highlighting the different groups or strongly distinctive species can display the difference in a less abstract fashion. Additionally, you could also select some species that seem to be abundant or often more absent in one group than the other. This could be extracted from the adonis function (but I am not sure anymore) could also apply the envfit function from vegan and select the species with the highest Rsq (https://www.rdocumentation.org/packages/vegan/versions/2.4-2/topics/envfit).

Considering the latter question. This depends on the question If you want to compare the two "treatments" and highlight the differences, you reached the goal by the above. If the question is related to potential causes for the differences you could perform an rda or cca and with a selection procedure find the predictor variable still considered "important" for between species variation based on the criteria used in the selection procedure (https://www.davidzeleny.net/anadat-r/doku.php/en:forward_sel_examples). Depending on the sample size you could apply a threshold analysis for a single variable that is known to affect periphyton and derive a threshold (https://cran.r-project.org/web/packages/TITAN2/index.html) shift between species along gradient can be expected. However, this depends on the question. I always find it a real challenge to keep analysis as simple and minimalistic as possible to still answer the question and provide the most interesting information.

Wim Kaijser thank you, your answer really helped me :)

Since Anosim did not tell me where the observed differences were, I also did a Friedman test with nemenji post hoc test (my data did not meet the prerequisites of Repeated measures ANOVA but was still sampled repeatedly during one year).

Now I am really not sure should I report Anosim results too? I did an NMDS biplot higlihting the significant intrinsic and extrinsic factors as you advised and it looks pretty good.

I would advise only using one, or else it gets too confusing. I am unfortunately not familiar with the Friedman test (perhaps someone else is more familiar with the Friedman test?). I do not know if this test fits, or has to fit with the results of the NMDS. What I know is it that ANOSIM can fit the dissimilarity matrix used for the NMDS. Thus, ANOSIM an the NMDS are comparable. Yet, if ANOSIM does not address your question another method might be just as suitable.