Step1:  Remove the Automatic ID from front end Property Page with custom CSS.

Add the below custom CSS in Theme Options > Design > Custom CSS:
#propertyid_display{
display:none;
}

Help article for how to add custom CSS
Step2: Add a new custom field for property custom ID go to Theme options >  General > Custom fields:

Help article for how to add Property Custom Fields


Step 3: Add field to the search form and use EQUAL as compare.

manual id search

Help article for Advanced Search Form Setup

This ID can be added in Admin when adding/editing property or in Front End submission form when submitting property.

Help article for how to add a property

Tip: If you have theme cache enabled, make sure you clear cache to see instant results.