Some random thoughts:
- Notes is not exclusively stored on your phone, or in iCloud.
- Notes can be part of your email provider's account. Gmail (as an external example) has Notes that can be turned on or off. Other providers have Notes. They show up just like your inbox, trash, etc. That is one way to have notes stored elsewhere.
- Notes can be stored in iCloud.
- Notes can be stored 'on your phone' but, not stored separately.
To start with troubleshooting:
- Do you have iCloud or iCloud+ (a paid tier)? If you have the paid tier, you can log into your iCloud account from a web browser. It doesn't even have to be an Apple device. Log into your account and look at your Notes. Are they there? If not, they are gone from iCloud.
- Do you think those notes were attached to your email provider account? Same thing: log into your email from a web browser and look for Notes in your folder tree. Make sure your notes are not in there.
If the notes were only stored locally and you told it to delete them from your iPhone, they are probably gone.
With all of that said: Notes, when connected to iCloud and synced across your devices, is one of the most powerful apps in the Apple ecosystem. Absolutely mind blowing. I would enable iCloud notes, shut off notes with all other providers and buy, buy, buy.
You enter something in your iPhone Notes and (depending on your cell connection) will instantly sync across all your other devices. I have notes available on my Watch, phone, iPads and Mac.
Same story with Freeform. The two of them completely transformed how I store my personal information.
Same story with Calendar and Reminders. They can tightly integrate with Notes and Freeform. Keep it all synced with iCloud.
I know that all seems a bit off the topic of your question but, for the small amount of space that notes take up, they are not worth sacrificing. I recently changed phones. The fate of the data on my old phone didn't even matter. The new phone pulled everything off of iCloud and I was back in business.
