How can I remotely reset my iPhone passcode without erasing the device?

The passcode is used to decrypt your data. With no passcode, your data cannot be decrypted.

You will need to remember the passcode, or reset the passcode and erase the device and restore your backup.

There is no means to back up the data of your device remotely.

What data is stored in iCloud will remain available, if you remember your Apple Account t password.

With a Mac or PC: If you forgot your iPhone passcode or your iPhone is disabled - Apple Support

Without: If you see an iPhone, iPad, or Apple Vision Pro unavailable message or Security Lockout screen - Apple Support

How to perform backups: Back up iPhone - Apple Support

Your iPhone’s passcode cannot be entered remotely as it is stored locally. To reset your iPhone’s passcode will require you to erase the device. And if after erasing your iPhone and setting a new passcode it still doesn’t allow you to enter the correct one, your iPhone’s display may be failing. That would require service at your nearest Apple Store Genius Bar, now whether you want to invest more money into your iPhone 6s as stated in your tagline may not be such a good idea.

If you forgot your iPhone passcode or your iPhone is disabled - Apple Support

Genius Bar Reservation and Apple Support Options - Apple

If you have forgotten your passcode, you have no choice. Apple does not have access to your passcode, it only resides on the device. See the information here If you forgot your iPhone passcode or your iPhone is disabled - Apple Support

Zachyy wrote:

Your iPhone’s passcode cannot be entered remotely as it is stored locally.

The passcode is not stored locally, or stored at all.

The passcode is used as a decryption key.

In the case of typical Apple security designs, the password or passcode typically decrypts a “keybag” containing the robustly-created data encryption and decryption keys, and the robust keys are used to access the data.

This “keybag” design allows the password or passcode to be easily changed without requiring the entire device to be decrypted and then re-encrypted whenever the password or passcode is changed.

In general, the password or passcode itself is not stored, or the password or passcode is hashed*, and the hash value then stored and compared. Outside of specific tools such as password managers, configurations with robust security seldom store cleartext passwords.

For this case, and given there is no passcode stored anywhere, the keybags cannot be decrypted, so the user data protected by those key bags cannot be decrypted. And there is no changing the passcode short of a reset.

Details start around page 100: https://help.apple.com/pdf/security/en_US/apple-platform-security-guide.pdf

*Password hashes are deliberately slow and resource-intensive algorithms, designed to make repeated guessing tedious and expensive, and to be exceedingly difficult to reverse back to the original password or passcode input.

No. Your only option is to erase and restore the device.