Re: Is there an easy way to search in Messages?
Yes. It's much easier to search Messages on Mac computers, where the search field is always visible (at the top in the sidebar). Else: You could keep less Messages on your iPhone.
You can choose how long iPhone keeps your Messages on the iPhone ... If you want to keep them forever, that's fine, but you do have other options eg: 30 days or one year.
To choose: Go to: Settings > Messages > Message History > Keep Messages option
Or, You can just delete some of those older messages if they are no longer needed on your iPhone, or if you would like to use the storage space they take up.
How to: Delete messages and attachments on iPhone - Apple Support
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Here's Apple's search method for iPhone Messages if you want to check :
Search in Messages on iPhone - Apple Support
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Re: " ... how can we get this feature redesigned for real world use?"
If you wish you can send feedback to Apple. They will likely not reply, yet if others are also experiencing a similar search issue and send feedback, there may be an update that addresses it.
Web-form for feedback: Feedback - Messages for iOS and iPadOS - Apple
All the best :-)