Scroll down to find earlier versions of Resolve & Fusion. Bear in mind that your database will have been changed by installing 16 so you will need to go back to your backed up database (the one you made before installing 16)
The version 16 database can't be read by the previous version 15. This is a typical ongoing issue when going backwards in any NLE software. The older can't read the newer versions files. That is true of the database and the individual saved project files.
I regularly backup my database and project files. I am about to play with Version 16 so I can jump back to an earlier version but any new work I do in 16 can't be opened in any earlier version. But I can go back to where I was with 15.
In sum: Resolve can simply export and import individual projects via a right-click in the Project Manager window.
Open the DR Project Manager window, right-click on a project and 'export' each of these in turn to the relevant media folder. That's pretty much exactly the same as a 'save as' in any other app. Project folders can then be moved around to other drives, backed up, archived etc. One tip: rename each of these files to be the same as the project name; Resolve defaults to naming each of these with a generic 'project' title. That wil help later (below) when you re-import each of these into a new DB.
Do that for all projects, here in this context or in any other for that matter. And that is a 'backup' beyond this DB versioning matter.
*Clean* uninstall DR Resolve 16 beta, ie, get rid of all prefs, related install folders etc. On Windows, something like 'IOBit Uninstaller' does a good job; then clean registry (say 'CCleaner'), then reboot. Same process for Mac OS, something like 'CleanMyMac' can do clean uninstalls. Otherwise, just do it manually if you know where to look in all the usual places. Delete all DBs for 16.
Reboot, install DR 15.3.1 (latest, very nice). Set up the various prefs as usual. Open the Project manager, then 'Import' individual projects by right-clicking on the Project Manager window space and selecting each of the above 'saved as' export files in turn. When that's all done, then there will be a full /new DB file again. Depending on the location of the original media files, you many need to point the project at the most recent path and/or link files in the Media page.