[1] Do these password managers even use their own keyboard, or rely on whatever insecure keyboard is installed on the mobile OS?
Many of them support biometric authentication using Android's API.
Also, to enter the master password, all of them use whatever keyboard is installed, some of them send a message to them to work in "incognito mode" for what good that it. That said, for Keepass2Android and KeePassDX, they offer their own keyboard to enter secure credentials on sites you log into once your password manager is unlocked. That allows you to circumvent the system clipboard entirely, which is a major attack surface. Some apps also support the android autofill feature.
Without typos? Typing a tweet or text message into your phone, your thumbs hit somewhere near the right characters and your phone figures out what words you meant as you type. The uncorrected characters are often gibberish. This is a very different use case from having to get the case and special characters right for a 40 character password.
Alternatively you can use fingerprint unlock
Fingerprint authentication will work though.
Am I misunderstanding the issue?
Bitwarden is able to produce diceware style passwords too.
And is this a known problem of Android, that there are keyboards that can log your keys?
Personally, I still like using Simple Keyboard. It's the complete opposite of something like Swiftkey. does one thing and does it well, is super light too.
[1] Also because I deal with work on my own time.
I do not trust any android device with my vault for exactly that reason.
Why is this relevant? Even if you do have secure enclave, if you can do arbitrary memory reads a malicious app can simply wait until your database is unlocked and dump your database when it's unencrypted in memory. Moreover, if you have some sort of exploit that gives you operating system level access, you can simply impersonate the password manager app (eg. changing uids, or patching the executable in-memory) and get the secure enclave to do the decryption.