New install of 2.4.4 and I'm not getting any email to users or form sendings. Using PHPMail or Sendmail I get no errors but also no email. SMTP gives an error can't find SMTP host.

The install is on a host with a temporary different domain and account domain name until the domain transfers. Wondering if this could be the problem because other 2.4.4 installations on the same host provider with matching domain names works?

Anybody else seen this? I don't want to build the whole site hoping this is the problem and then still have the problem when the domain name transfers...

I bumped into a similar problem before. On my host, you have to have the "Admin mail address" to have the same domain name as your current domain. Also, I can only use sendmail on my host. Hope this helps.

Same here.

You can try:
tail -200 /var/log/syslog | grep mail

(or some similar pattern that works out for you) to locate the problematic lines. In my case:

Apr 7 23:20:51 cachogordo postfix/qmgr[2287]: 2D750378714: from=, size=1123, nrcpt=1 (queue active)
Apr 7 23:20:51 cachogordo postfix/error[8296]: 2969B379145: to=, relay=none, delay=0.13, delays=0.06/0.01/0/0.06, dsn=5.0.0, status=bounced (gmail.com)
Apr 7 23:20:51 cachogordo postfix/error[8298]: 2D750378714: to=, relay=none, delay=0.12, delays=0.09/0.01/0/0.02, dsn=5.0.0, status=bounced (gmail.com)

(xxx and yyy conceal the real addresses of course)

So here it seems to be bounced by gmail.com
I set up gmail's server data in the Site Preferences / Mail Setup values:
mail.google.com
"username"
"password"

But still get the same output.
Any idea?

Because of the risk to be abused by SPAM, in general, gmail and other generic mail servers block mail sent from and/or through other domains.

Mosttimes your domain, comes with a own mailbox. Try to use this email account as explained by yingzhao.