To implement this requirement, you can refer to my steps below:
1. Use "List blobs" to list all of the blobs in your folder in storage.

2. Then add "For each" loop in your logic app to loop the value from "List blobs". And in "For each" loop, use "Insert row(V2)" to insert each file name into your sql table.

By the way, before the step2 I have already created a table named FilesTable
in my azure sql db like below screenshot:

And when you use "For each" loop to insert the rows, it's better for us to enable "Concurrency Control" and set Degree of Parallelism
to 1
to escape concurrency issue. Please do it as below:

