Open your Shields panel (lion icon in address bar)
Change cookie setting to Allow all cookies and allow the page to refresh
Now login to gmail and set the cookie control back to Block 3rd party cookies (if you so desire)
You are not saving your login credentials in-browser (or into any other password manager) for Brave to remember. If this is the case, make sure to save your login data in Brave (or preferred manager) so that it can be remembered the next time you need to access the site.
I have never saved my passwords online with any browser. I kept working–opening, signing in, closing–until finally it worked and kept me signed in. I have no idea what caused it to suddenly start working, and I thank you for your attempts to help me!