How secure are public hashed passwords (with a salt)? I'm working on a blockchain-based distributed application which stores Client information. I'm thinking of alternate ways to authenticate Clients on the network. One idea I got was to associate a Username and Password with the Client data structure -- where Password is a Hash(salt+password) where salt is securely stored only with us (the blockchain operator).

The clear security concern is that all participating members in the network can now view the hashed version of these passwords -- so how secure is this? Are there any other approaches I should be thinking about?
The main problem will be the password policy and users. If you let the users to choose any password, then they will tend to use 1234 as a password. A malicious user in your system can easily bruteforce all widely used insecure passwords. If you have a good policy, the only way is brute-forcing since we cannot reverse the hash and the salt prevents rainbow tables. For a general guideline for passwords, see NIST Digital Identity Guidelines 800-63B.

While considering the attack risks, we already assume that an attacker access the database of the users and we design our password systems as a last defense against the attacker. According to this, we design our system not by security by obscurity. So, you already in this stage.

Actually, we don't use a simple hash technique to store passwords. For example, iteration as in PBKDF2 can decrease the time of the attacker like 10000 times. Also, you need to protect against massive parallelization as in GPU usage of hashcat.

You should use PBKDF2, Bcrypt, or better argon2  which is the winner of the password hashing competition.

Also, for general advice see the How to securely hash passwords? from Information Security.