The BPS Security Log logs all 403 errors whether or not BPS is blocking something. So if something else is blocking the PHP Info Viewer then BPS will log that 403 error. If you turn Off Security Logging and try to use the PHP Info Viewer tool then instead of the BPS Security Log logging the error you should see a server error message, which may tell you more information about what is blocking the PHP Info Viewer or you may just see a default server 403 error message page.
There is a new version of BPS Pro available: 14.1. The Security Log entry shows that you have BPS Pro 14 installed.
The Server Protocol is HTTP/1.0, which usually indicates that you are using a Proxy or Load Balancer, but the HTTP_X_FORWARDED_FOR Security Log field does not show a Proxy/Load Balancer IP address. Are you using a Proxy or VPN Browser on your computer?
You can test both PHP mail() and WordPress wp_mail() by using the S-Monitor > Simple Email Tests tool. You should run the Setup Wizard if you have not done that already when you switched your hosting server. If you are able to successfully send emails using the Simple Email Tests tool then the next thing to check would be WordPress standard crons. ie if you have disabled WordPress standard crons then you will not receive emails from S-Monitor/BPS, unless you have setup a Direct Cron correctly. Correctly being the key word here. ie Direct Cron jobs should be set to run once per minute. Any other time interval is a mistake for Direct Cron jobs.
There is another possible cause for the 403 error, but I need to know where Server Protocol HTTP/1.0 is coming from. ie your server/Proxy or your computer/Browser.