Authentication app is another option. I believe some password managers can be set up to take the master password once per device and then accept authenticator codes to unlock for each subsequent time.
Or, since your phone is probably a lot more locked down than your computer, almost every modern phone since like the days of the iPhone 5S has a cryptographic TPM/secure enclave in the processor while the fact that not every computer has one was a major sore spot in Windows 11 compatibility, it might also be acceptable to just leave the password manager unlocked on your phone all the time, depending on your threat model. Assuming your phone is both encrypted and password protected and you trust the OS to implement both securely, the pin on your phone works more like the pin on your credit card than a traditional password login on a non-encrypted non-TPM computer, so even if a bad actor physically had your phone, it would be very hard to actually extract data out of it without the passcode (assuming it’s just your garden variety cybercriminal and not the CIA or something), which would serve as your master password in that case. Hardware security features can also resist brute force attacks where someone clones your hard drive and hooks it up to their own computer to try and guess the encryption password without the wrong entry time delays slowing them down, a secure enclave will actually enforce the time delays with no easy bypass and can also be set to wipe the phone if you get the passcode wrong too many times.
Phone apps are also almost entirely sandboxed from each other and can’t directly access other apps’ data, so the risk of a malicious program reading the password manager’s cache or database is also far lower than most desktop operating systems.