After some health problem I have lost the private key but I still have the password.
If you don't have the wallet file, the password is useless, as the password only encrypts the file.
If you don't have the wallet file + password, or the private keys, there is no way whatsoever to recover your coins. Sorry for your loss.
There is any way to recovery my Bitcoin?
No. If you want to have any hope of recovery, you need a backup of your wallet file.
As I understand after extensive search it seems to be hard to find the private key of my own BTC address but i fund an interesting site called https://privatekeys.directory/ where seems to be possible to find (theoretically) any private key.
That site is a (possibly cruel) joke. Yes, it lists all private keys, but in order of increasing private key. It cannot search by public key. Since there are 115,792,089,237,316,195,423,570,985,008,687,907,852,837,564,279,074,904,382,605,163,141,518,161,494,336 valid private keys, and 25 keys per page, you'd need to scroll on average through 2,315,841,784,746,323,908,471,419,700,173,758,157,056,751,285,581,498,087,652,103,262,830,363,229,887 pages before you'd encounter your key. That number is enormous. Even if you had every human on earth go though it, at 100 pages per second, it would take billions upon billions upon billions of times the age of the universe before you had any chance of hitting your key. To be clear, the site just computes the keys on the fly as they are requested. They do not have a full database of all keys - such a database can simply not be constructed.
