Yes, it is possible to manually install an APK to the work profile or any other user present on the Android device via ADB.
Enterprise policies may prevent the installation of applications via ADB, please ensure your device is excluded from any such policy before continuing.
Be aware that since Android 14, it is no longer possible to install very old applications on a device. Via ADB you can overcome this, if necessary.
First, locate the user ID of the profile or user you wish to target:
adb shell pm list users
This will output a user list of all users on the device, for example:
UserInfo{0:Jason:4c13} running
UserInfo{10:Work Profile:1030} running
UserInfo{11:Private space:1090}
Besides the primary user, which is always userID 0, the above example also shows a Work Profile and a Private space (Private Space is Android 15+)
With the appropriate userID identified, install an APK as follows:
adb install --user 10 /path/to/yourfile.apk
Your application should install, and appear shortly within the appropriate profile.