Adding a “password” path is actually only increasing your security by a constant factor per character because of the risk of timing attacks (unless you are sure that the path matching algorithm is secure against it now and in the future). Ideally a 2nd layer would guard against it in a multiplicative way (an entirely different with system).

Cryptographically, adding characters to the password rather than to the path is better (because it increases the search space exponentially) than adding characters to the path, which can be brute forced separately per character.

But this assumes a very perfect view of software, where there are no bugs. Once you add a risk model for bugs, then there might be small values of path length where the additional constant factor is better than the multiplicative one that you get from adding characters to your password. So your rebuttal holds, depending on the exact bug risk model you have.

I think nowadays, tailscale/wireguard is really convenient and pretty secure as a 2nd layer. I was averse to self hosting my password manager in the past due to not being comfortable having the consistent time to secure more critical applications, but I might actually move to a world where I host more critical things myself behind a VPN.