When I use URL Inspection/Test live URL In google search console I am getting “Blocked due to access forbidden (403)”, but this error does not show when I use Pause Cloudflare on site function in Cloudflare dashboard, please let me know what is the problem, thank you.
Did you get a response from Cloudflare about this issue? Thanks.
Did you checked at Cloudflare dashboard → WAF → Overview for any Firewall event which might occur to figure out which Cloudflare service did presented a challenge or blocked the particular request? 
You can inspect even the IP, ASN, User-agent and more information.
Can you provide us with some feedback information here about this?