Yeah you need to update more than just the siteurl values if you wish that every reference (post and attachment included) are updated properly.
And you can’t update that with simple SQL queries because you are going to break the serialization of arrays.
The best thing you can do is use Search Replace DB.
Download the script from github, upload it to your server to a subfolder. For instance, https://example.com/searchdb and follow the instructions there.
You simply need to search for http://example.com and replace with https://example.com. But you can search and replace pretty much anything in your database.
Keep in mind that this will perform queries in your database and edit stuff… so you better keep a good backup of your database, in case something goes wrong.
I never had any issues with the script, it works perfectly… but better be safe than sorry.
One last thing… REMEMBER TO DELETE THE SUBFOLDER AFTER USAGE. You don’t want the script to be laying around on an open server !