For such suggestion I think it must be asked on MSE, but please validate if it was already asked in the past there. I would not migrate directly as often duplicate get downvoted a lot on MSE
I think the rational of MSE is you can be a good programmer, but a total outsider to be a sysadmin, thus the right gain are by site.
A good exemple; I'am French native and my reputation here is good, but giving me the editing right on like English Language and Usage would not be ok, as I'am far to be the best in English.
In your case it's borderline as tag like mysql are shared between DBA and here, and often a DBA question could fit both site. (but on StackOverflow the tag would possibly mean more the API side of the product) So maybe there is a case to do on MSE when a site share some tags on sisters site like you state, but I will leave you the choice to post the feature-request on MSE or not.