And i compared to other papers and, mine is much higher . I know that shannon index calculation can vary in terms of log right? If that is so, how i do compare?

Another question, the value of shannon index is the median right? (in the boxplot), how do i know the mean value?

Hi! Each box plot shows you the range of Shannon indieces for all your samples within certain group, with a mean indicated as well.
The value of Shannon index can vary because of the source of your samples. In my case I have 4 different sources and Shannon index varies significantly between them.

A bunch of things can affect the Shannon index. Switching from OTUs to ASVs can change it.

The Shannon index uses a log scale, but it can use log2 or log10 or natural log, and all of these are perfectly valid nobody EVER reports which one they are using!

This sounds crazy. And it is. And yet if you look in the original Shannon entropy paper that has 69,200 citations, all three of these log bases are mentioned on page one:

The choice of a logarithmic base corresponds to the choice of a unit for measuring information. If the base 2 is used the resulting units may be called binary digits, or more briefly bits...
If the base 10 is used the units may be called decimal digits...
In analytical work where integration and differentiation are involved the base e is sometimes useful.

The Shannon index is totally arbitrary, but the difference in Shannon index between groups matters. I think you can safely report that the Shannon diversity is not significantly different between these two oral microbiome samples.

Not to mention your sequencing platform, rarefaction depth, and seemingly, sometimes the phase of the moon ( )... okay probably not the last one, but it sometimes feels like that!

I actually think the absolute value of your alpha diversity isn't worth much. As Colin said, it's so sensitive to each experiment. I've tried to move away from reporting (or showing) the actual number for alpha diversity in my analyses and have been trying to show it as a z-normalized value. For my case control study, that means my new alpha diversity is \frac{a - \mathrm{mean}(a_{control})}{\mathrm{std}(a_{control})}. It works okay if my data is asymptotically normal (which is true for my larger case-control studies) and helps get my collaborators and I away from the trap of giving the actual numeric value too much emphasis. (Although I will also say I do this with the alpha diversity export rather than the raw visualization.)

You want the alpha diversity .qza (i.e. shannon.qza). You can do that via the python API, qiime2R, or simply using the export functionality depending on how you want to process.