Although the question is about progress towards the specific badge, based on the comments added by the OP, it seems the main question is how to run SEDE queries when you want a look at a specific site (in this case MathOVerflow) and on a specific user.
The OP provided this SEDE query: Socratic badge progress.
- Notice that every SEDE query can be run on different sites - you have to choose MathOverflow. (You can also choose MathOverflow Meta and various other sites.)
- The query has a parameter userid - where you have to enter your userid.
- You should also keep in might that the data in this database are only updated once a week.
- As a side note, it is slightly better to be logged in on SEDE. (So that you do not have to solve a captcha when running a query.)
The userid is the number you can see in the URL and in the search bar when you go to your profile page. (If you have accounts on several sites, userid on each of them will be different.) More details on this: What is my user ID?
Regarding the original question about badge progress towards the next Socratic badge, it might be useful to add some links.
- There is the following feature request on Meta Stack Exchange: Track next Socratic badge progress. In fact, Glorfindel's answer to that question contains precisely the query mentioned above. (And it also mentions the warning that the query will not be precise.)
- There is also this post on Meta Stack Overflow: I would like to track my next Socratic badge. And one more related post on Meta Stack Exchange: How can we see our progress towards the next Socratic badge? In both cases, you can find some SEDE queries in the answers.