Mojolicious itself does not seem to use Perl threads.

% git remote -v   
origin  git@github.com:mojolicious/mojo.git (fetch)
origin  git@github.com:mojolicious/mojo.git (push)
% ls           
Changes  examples  lib  LICENSE  Makefile.PL  MANIFEST.SKIP  README.md
+  script  t
% rg 'use threads'
% rg 'threads'    
%
[download]

The SQLite docs indicate it may not be suitable if your workflow involves a high degree of concurrent writing, but you'd need to assess/test if you're likely to reach that point.

Using Time::HiRes, you could check how expensive getting the handle really is. Chances are it may not be significant.