DaVinci R 17: Error while saving the project

Welcome as a new member
if you chose Da Vinci it's to improve your video editing skills you already made a mistake:
you uninstalled your software and thus eliminated all chances of recovering your project
uninstalling a software is a complex thing you also need to eliminate all traces of mini files from the software a clean reinstallation depends on it
the software uses music and video files present on your hard drive so they are virtual in the software
by uninstalling the software you clear the auxiliary memory of the software
for the future if you have an anomaly when saving you need to check the thumbnails of your project and the transitions which might be too short in time your timeline and pass for a line you must therefore lengthen the timeline at the cursor to locate these micro files that block finalization
this is often due to poorly made cuts where we leave a part of the file too small to be finalized
I’m copying this summary as well:
System restore to an earlier date
in case of persistent bugs think before upsetting your computer to perform a "system restore to an earlier date" (before the bug) this is the Windows term it aims to bring your system back to the state before the bug it's risk-free and reversible and often beneficial ,
Go to "Settings" in the box type "restore"
In the dropdown click on "create a restore point"
Click on "system properties" system restore
In the box click on "next"
Choose a date prior to the day of the bug
next …….. allow time for calculation ….
Ps: when you wish to install a software or an application, it is wise to first create a restore point with a name it will be useful in case of failure or change of mind to return to the previous state before the installation the note that Windows also creates automatic dates that you can use if needed

I speak from experience not from theory good luck

"Donkeys change their minds not fools"
remember to mark "resolved" on your message if that's the case