I’ve been using Brave Beta for months on my M1 MacBook without issues. This morning when I checked for an update, the update file downloaded and installed, but it immediately crashed after launching (the browser window flashes momentarily, but then the desktop appears). I restarted the MacBook, downloaded Brave Beta again, replaced the existing Beta installation with the new file, and the same thing happened. To rule out an issue specifically related to my laptop, I downloaded and installed Brave Nightly and Brave Release Channel, and both installed and launched without any problems.
UPDATE: I was able to launch Brave Beta by opening a local html file stored on my MacBook. I checked for an updated version of Brave Beta, and downloaded the update (1.44.79) hoping it was just a bug that was fixed. I relaunched Brave Beta to complete the update, and it immediately crashed again.
The bug appears to be related to opening a new tab with remote content. I can load a local html file and then click on a bookmarked page, and Brave Beta will load the remote website and new content. But any time I click a new tab, it crashes. And Settings > Get Started > On Startup selection makes no difference. Brave Beta crashes whether I have selected Open the new tab page, Continue where you left off, or Open a specific page or set of pages. Yes, I could select the 3rd option to open Brave Beta using a local html file, but I cannot open a new tab ever, or the browser immediately crashes…so the 3rd option isn’t much of an option 
UPDATE #2: I found a solution here. I have no idea what changed this setting on my original Brave Beta installation, because I don’t tinker with browser flags. But setting this flag to “default” appears to resolve the issue, and Brave Beta opens new tabs normally again.