Temporary .htaccess blocking is disabling WP Crons from running?

The .htaccess directives block any HTTP request not coming from your IP address. However, I believe WP Cron is also an HTTP request that originates from the server. So, you need to also make an exception for the server’s external IP address.

These directives can also be simplified a bit…

For example:

RewriteCond %{REMOTE_ADDR} !=203.0.113.111
RewriteCond %{REMOTE_ADDR} !=11.22.33.44
RewriteRule !^brb/ /brb/index.html [R=307,L]

Where 203.0.113.111 is whatever your server’s IP address is.

The = operator on the CondPattern makes it a lexicographical string comparison, as opposed to a regex, so no need for the start-of-string anchor (^) or escaping of literal dots (which you aren’t doing anyway, but strictly should be).

No need for the additional condition that checks that the URL-path does not start /brb/, since this can be incorporated into the RewriteRule pattern. (And no need for the capturing groups, since you don’t have any backreferences.)