Two versions of Da Vinci Resolve hold different projects

First issue:
As a result of an update, I have two versions of Da Vinci Resolve 19 (19.1.3 build 7 and 19.1.4 build 11) installed alongside each other on MacOS.
The older version knows about the most recent project I've been working on, which is stored with all its media on a separate hard drive. This is the project I need to continue working on.
The newer version knows about all the other projects I've had, which are on the laptop's internal disk. All of those projects were built with the older version or some version even older.
Why doesn't the newer version know about the most recent project?
Why doesn't the older version know about the other projects it was used to build?
Is there a way to have the newer version also include the most recent project in its database, so I don't need to keep the older one around?
Second issue:
Although there are about a half dozen projects presented in the Project Manager of one version or the other, and there are project backup folders corresponding to each, there seems to be only one .drp file on the machine. Is there supposed to be one .drp file for each project that could be opened in the app? If not, how are the projects stored and found by whichever version of the app I run.
As a result of an update, I have two versions of Da Vinci Resolve 19 (19.1.3 build 7 and 19.1.4 build 11) installed alongside each other on MacOS.
The older version knows about the most recent project I've been working on, which is stored with all its media on a separate hard drive. This is the project I need to continue working on.
The newer version knows about all the other projects I've had, which are on the laptop's internal disk. All of those projects were built with the older version or some version even older.
Why doesn't the newer version know about the most recent project?
Why doesn't the older version know about the other projects it was used to build?
Is there a way to have the newer version also include the most recent project in its database, so I don't need to keep the older one around?
Second issue:
Although there are about a half dozen projects presented in the Project Manager of one version or the other, and there are project backup folders corresponding to each, there seems to be only one .drp file on the machine. Is there supposed to be one .drp file for each project that could be opened in the app? If not, how are the projects stored and found by whichever version of the app I run.