Accessing certain fields from another Eloquent model

I am having such a terrible time trying to achieve a certain thing – I have a model A that needs to access model Profile’s column name for search functionality, but I have been getting all of A instead of “no search returned” or the specific search list. I am new to PHP.

Here’s my code.

// Model A (excerpt) (Models.php)

class A extends Model {
    public function user()
    {
        return $this->belongsTo(User::class);
    }

    public function profile() {
        return $this->hasOneThrough(Profile::class, User::class, 'id', 'user_id', 'user_id');
   }
}

Model Profile

class Profile extends Model
{
    use HasFactory, UuidTrait;

    public $guarded = ['null'];

    public function user()
    {
        return $this->belongsTo(User::class);
    }
}

// my error is coming from below

UserController.php

....
if($search != "")
{
    $users->orWhereHas('A', function($query) use($search) {
       $query->where('A.first_name', 'LIKE', "${search}%"
    }

}

Model A columns: id, user_id, address, size
Model Profile columns: id, first_name, gender, user_id

Hence, the relationship of A to Profile is through user_id (say, A=>user_id=>profile.first_name)

Expected Result:

search ‘Fred’ (present in Profile)
return A fields with ‘Fred’ present

Actual Result:

no column A.first_name