It's disappointing to hear that the Yubikey/PasswordSafe interface worked that way. I don't own a YubiKey, so I haven't been able to try it. I don't know whether it has changed.
(After doing a quick search...)
The program history
claims it was added to the main PS program in v3.32 in 2013 (having been previously usable via a separate branch in 2009), and mentions "yubikey" (search was not case-sensitive) only a few times since then. No update during 2020 contains "yubikey" and the mentions over the intervening years are pretty sparse (v3.34 
, v3.34.1 
, v3.35 
, v3.37 
, v3.47.0 
). AFAIK, the current Windows version is v3.53.0, released on 2020-09-08.
that "Password Safe uses YubiKey’s HMAC-SHA1 challenge response mode
" and "[b
]oth a master password and a YubiKey are needed to enable access to your Password Safe file
[. . .]"
Likely due to my inexperience with YubiKeys, I don't know whether that differs from the method you described.