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When you ask Joomla to install an extension you send an HTTP POST request from your browser to your server. Your site's server rejected that request with an HTTP 413 error. This means that you have a web server configuration issue.

The reason I cannot help you is that the HTTP response you got did not come from our site. The HTTP 413 comes from your own site's web server. I cannot help you fix your web server. That's what your host has to do. It's part of the service you pay them for.

While there is a workaround, I am not sure it will work. You can try. Log into our site. Go to our Download page. Click on the “Release notes and all files for version 9.9.11” link underneath Akeeba Backup's downloads. This currently leads you to https://www.akeeba.com/download/akeeba-backup/9-9-11.html. Right click on Direct Install Link. Copy the link. Go to your site's administrator, System, Install, Extensions, Install from URL and paste the URL you copied in the provided box. Click on Install. This instructs Joomla to connect to our server, download the ZIP package, and install it.

IPv6 could cause problems with the TLS certificate if it's pinned to a specific (IPv4) address. It could not cause the HTTP 413 issue. That's something which can only happen with the web server configuration. On Apache you can use the LimitRequestBody directive to reject requests whose request body is over a limit. Would you guess what is the HTTP response for that? HTTP 413 Content Too Large.

What I think happened is that your host still lives in 2004 when a 2MB upload limit was workable, or you followed a tutorial by someone who stupidly sold you that kind of upload limit as a security feature (it's not; it will cause you to circumvent the restriction with FTP/SFTP, leading to even less security and a lot more anguish). Can you please ask your host where the LimitRequestBody directive is and increase it? As to how much to increase it: I would go with 48MB which is what you need to upgrade between Joomla major releases in case fetching the update package over the web fails.