Yes, you can solve almost anything with Script Runner (in JIRA, Bitbucket or Confluence at least), but I thought that this was more of a one-off correction than something you'd do a lot. I'm not sure there's a good use-case for doing this a lot, it feels a bit like a broken process.
But, I suspect you can still do it. The latest versions of SR allow you to insert simple hooks into the interface as buttons. I have only used them a bit, and I don't know if they can do the "input field" bit, but they can certainly trigger the scripts, and with a script, you can go read all sorts of stuff as input. So I know you can get close.
(Apologies if this feels like an advert - I do work for Adaptavist, SR is one of our flagship products, and hence I use it a lot. This really is one where SR feels right, and if I didn't work here, the only change I'd make to this answer would be to drop this comment about working here!)
And potentially destroy your installation. SQL on a JIRA database is to be avoided at all times. Always use the API. If you must use SQL, plan to shut it all down and take a backup before risking it, and then factor in the time for a full reindex afterwards.
There is a way to bulk edit (replace) issues summary, I use - via Jira Automation Plugin.
you just need to make automation rule (scheduled by cron for example)
add there jql query like in jira filters, and add the action, you need to perform - edit issue (change summary),
and then start the rule manually, or wait until it starts automatically.
Another way is to use script runner, as mentioned by Nic Brough [Adaptavist] the idea is same.
Nice hint with scheduled job, thank you Pavel!
For all the people who'd like to go on with this approach - keep in mind that if you have a notification scheme configured for your target project, this job will fire email notification on "issue updated" event for each issue you update this way.