macOS Catalina(10.15.3)で、Homebrewで入れたApacheが起動しない問題への対応

# ブラウザでlocahostにアクセスしても何も表示されない
$ sudo apachectl start

$ view /usr/local/etc/httpd/httpd.conf
...
ErrorLog "/usr/local/var/log/httpd/error_log"
...

$ tail -1000 /usr/local/var/log/httpd/error_log
...
[Wed Feb 05 22:33:14.400907 2020] [ssl:warn] [pid 20851] AH01873: Init: Session Cache is not configured [hint: SSLSessionCache]
[Wed Feb 05 22:33:14.401430 2020] [cgid:error] [pid 20852] (2)No such file or directory: AH01243: Couldn't bind unix domain socket /usr/local/var/run/httpd/cgisock.20851
[Wed Feb 05 22:33:14.402081 2020] [http2:warn] [pid 20851] AH10034: The mpm module (prefork.c) is not supported by mod_http2. The mpm determines how things are processed in your server. HTTP/2 has more demands in this regard and the currently selected mpm will just not do. This is an advisory warning. Your server will continue to work, but the HTTP/2 protocol will be inactive.
[Wed Feb 05 22:33:14.402221 2020] [lbmethod_heartbeat:notice] [pid 20851] AH02282: No slotmem from mod_heartmonitor
[Wed Feb 05 22:33:14.403549 2020] [core:error] [pid 20851] (2)No such file or directory: AH00099: could not create /usr/local/var/run/httpd/httpd.pid
[Wed Feb 05 22:33:14.403572 2020] [core:error] [pid 20851] AH00100: httpd: could not log pid to file /usr/local/var/run/httpd/httpd.pid

# runディレクトリ以下には何もない
$ cd /usr/local/var/run
$ ls -la 
total 0
drwxr-xr-x  2 username  admin   64  2  5 22:33 .
drwxrwxr-x  9 username  admin  288  2  5 22:33 ..

# httpdディレクトリを作成
$ mkdir httpd
$ ls -la
total 0
drwxr-xr-x  3 username  admin   96  2  5 22:35 .
drwxrwxr-x  9 username  admin  288  2  5 22:33 ..
drwxr-xr-x  2 username  admin   64  2  5 22:35 httpd

# ブラウザでlocalhostにアクセスできるようになった！
$ sudo apachectl start

# cgisock.21666 と httpd.pidが作成されている
$ ls -la /usr/local/var/run/httpd
total 8
drwxr-xr-x  4 username  admin  128  2  5 22:35 .
drwxr-xr-x  3 username  admin   96  2  5 22:35 ..
srwx------  1 _www      admin    0  2  5 22:35 cgisock.21666
-rw-r--r--  1 root      admin    6  2  5 22:35 httpd.pid