This release includes a major change. The plugin will no longer use Google Chrome, Chromedriver and Selenium to interact with browsers. Instead, the plugin will now leverage Puppeteer.
Previously, when Google Chrome was updated the plugin would break because the Chromedriver installation used by the plugin would no longer be compatible with your updated version of Chrome. This was resolvable by updating Chromedriver wherever you globally installed sfdx which was not entirely intuitive. When you install the new version of the plugin, Puppeteer "downloads a recent version of Chromium (~170MB Mac, ~282MB Linux, ~280MB Win) that is guaranteed to work with the API" so the Chrome update bug no longer persists.
Puppeteer's API also includes some great capabilities that will also make this plugin faster and if you want to use the plugin in CI/CD processes you no longer need to install Google Chrome beforehand.
To update the plugin, I think you can run sfdx plugins:update but it may be safer to run:
sfdx plugins:uninstall sfdx-deliverability-access && sfdx plugins:install sfdx-deliverability-access