red1234,
I saw the screenshot.
The following is lengthy. Please read carefully. Getting familiar with all the locations of the items mentioned, will help you a lot, before taking steps.
Some of this may be familiar to you, but I do not know how familiar you are with your Mac. So . . .
Please Quit all Brave Browser applications.
Where some things are at, using Mac OS X:
Root: simply a forward slash /
Root and System level folders
/
/Applications/
/Library/
/System/
/Users/
The “Brave Browser.app” application is located:
/Applications/Brave Browser/
There, and hereafter, I am referring to the location of files and folders - assuming a stable release of Brave Browser is/was the only installed version. (No Brave Browser Beta’s. Nor Nightlies.)
Your machine user account folder, aka home folder “your_username_aka_shortname”:
/Users/your_username_aka_shortname/
Therein (of interest today):
/Users/your_username_aka_shortname/Desktop/
/Users/your_username_aka_shortname/Library/
Caches
System level Cache files - generally you do not mess with these very often:
/Library/Caches/
On the other hand, your user account “Library” folder and its “Caches” folder:
/Users/your_username_aka_shortname/Library/Caches/
Generally, therein, you can - after quitting associated/relevant application(s), move your cache files n folders that you select
/Users/your_username_aka_shortname/Library/Caches/< files n folders >
to the Trash. For example, there are (Mac OS 10.12.n Sierra) two Brave Browser cache directories that could be moved to the Trash, “BraveSoftware” and “com.brave.Browser”:


Application Support
System level Application Support:
/Library/Application Support/
Currently (Sierra example) - there is no “Brave Browser” type folder therein.
On the other hand, in your user account’s Application Support:
/Users/your_username_aka_shortname/Library/Application Support/
might have a Brave Browser folder named “BraveSoftware”
I suggest that you Compress (.zip) that “BraveSoftware” folder (if it exists on your Mac - you might show a different folder name). The Compress command is under the File menu of the Finder. First, select the folder that is to be .zip compressed, and then under File (menu), select Compress. Give the resulting .zip file, a name showing the date; for example: “BraveSoftware_20210823_Monday.zip” . . . and thus, you have created a backup, “just in case.”
Next, let’s take a look within:
/Users/your_username_aka_shortname/Library/Application Support/BraveSoftware/
And therein, a sub-folder “Brave-Browser”:
/Users/your_username_aka_shortname/Library/Application Support/BraveSoftware/Brave-Browser/
And, therein, several files and folders . . . something to consider:
Recently (last few days of the 2nd week of August 2021) there were some temporary fixes / solutions to Brave Browser problems (for some users), where CPU/RAM usage has been high, and/or failure to successfully start Brave Browser (crashes or freezes).
Among the temporary fixes, were TWO that might apply to your situation (though their influence may not be apparent on the surface of what is happening with your Mac). So, after Quitting Brave Browser:
ONE: Move to the Trash, all the contents within the “CertificateRevocation” folder (but not the folder itself):
/Users/user_shortname/Library/Application Support/BraveSoftware/Brave-Browser/CertificateRevocation/
TWO: Move to the Trash, the “cffkpbalmllkdoenhmdmpbkajipdjfam” folder:
/Users/user_shortname/Library/Application Support/BraveSoftware/Brave-Browser/cffkpbalmllkdoenhmdmpbkajipdjfam/
Example screenshot of both a) the contents of folder “CertificateRevocation” and b) the “cffkpbalmllkdoenhmdmpbkajipdjfam” folder, currently:

You might take a swing at THOSE TWO TEMPORARY FIXES just mentioned . . . AFTER you:
First, Repeat reminder to Quit Brave Browser (including any Beta’s, Nightlies).
Second, un-install whatever Brave Browser applications you may have installed by now.
Third, move to the Trash, the aforementioned cache collections of your user account on your Mac.
Fourth, Locate the Preferences file “com.brave.Browser.plist” for Brave Browser:
/Users/your_username_aka_shortname/Library/Preferences/com.brave.Browser.plist
And move that “com.brave.Browser.plist” file to the Trash.
Restart your Mac.
THEN, after all that cleanup, install the latest stable release of Brave Browser:
“https://brave.com/download/”
IF THEN, the latest stable release of Brave Browser will NOT install, you will need Brave Support help, directly.
Because probably a required signature credential for the Installer (or some part thereof), is not correct, or some Bundle Identifier info, is not correct (something like that) - would be my guess.
(PS. Sometimes, the date info, of your computer, might be off enough, such that an installation will not proceed.)