I've attached a patch to address this.

The issue is that ob-sqlite.el uses org-babel-string-read, which purposefully removes double-quotes. I think this is unintended behaviour, and it only seems to be used with ob-sqlite.el. I added a minor function to bypass the part of org-babel-string-read that was stripping out the double-quotes and use the rest of the function.

I tried ob-sql with the mysql engine and didn't experience the same bug, so I'm pretty confident that this is an isolated issue.

I am using Org mode version 9.4.5 (9.4.5-73-g4c7696-elpaplus and I have the following code snippet. Values in the 'sql' column of the second row is truncated. Am I missing something?

#+begin_src sqlite :db /tmp/rip.db  :colnames yes
  drop table if exists testtable;
  create table testtable(id int, sql varchar);
  insert into testtable values (1, "Select id from foo");
  insert into testtable values (2, 'Select "id" from foo');
  select* from testtable;
#+end_src

#+RESULTS: testsql
| id | sql                |
|----+--------------------|
|  1 | Select id from foo |
|  2 | id                 |