Re: "Messages storage issue, 4.59 GB used despite deleting my messages"
"Recently Deleted is completely empty"
Seems you must have permanently deleted the messages.
Delete messages and attachments in Messages on iPhone
Eg: says:
"Deleted messages and attachments remain in the Recently Deleted folder for 30 days, but you can permanently remove them before that.
- Go to the Messages app on your iPhone.
- In the conversation list, tap the (three lines icon), then tap Recently Deleted.
- Select the conversations whose messages you want to delete permanently, tap bin icon, then tap Delete.
- Important: This can’t be undone.
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Re: " ... ... However, Messages still uses 4.59 GB in total!"
You might want to try restarting your iPhone, (ie: deletes temporary files, re-establishes connections, may update recent setting changes etc, and often restores order if something is not working as expected.)
If needed: See how to: Restart your iPhone – Apple Support
and
How to check the storage on your iPhone and iPad - Apple Support