Updating an old version of Brave (for Mac) -- when downloading is the correct version determined automatically?

Take a look a the command line method for starting up Brave Browser:

You might get the Beta version of Brave running, and then back up your bookmarks and passwords.

And, if the “existing Release version” can also work, back up your bookmarks and passwords.

After saving all that data, remove the items - re the locations listed above.

Then make an effectively fresh installation, using the workable version of Brave Browser.