Clear your cache files and cookies, and then try to go manually to
https://Myemail.cox.net
I tested it on my mac with Safari and Opera. Both worked fine, and I am on the new webmail.
Additionally, They don't charge you for webmail, HOW can corporate greed even figure into this picture?
If you are talking about Internet speeds, what modem are you using and have you tested your speed with a computer connected via ethernet, since testing over WiFi is inaccurate.
If you want assistance in addressing your issues, there are several of us here that between us, we have DECADES of experience, and we will be glad to help, unless you are here to slander, cast aspersions, and kvetch.
I have the preferred internet which has been upgraded to 500 down/50 up. With the right equipment and settings -
https://www.speedtest.net/result/14968027172
Over WiFi. It can be donw, but I installed some fairly expensive equipment, a CM2000 Modem, and since the router I bought died, I went ahead and installed a RAXE300 Netgear. The test you see was done using WiFi 6.