Here are the access logs for the provider moodle if that is important:
When the "Embed" option is selected it goes directly from course view to login:
"POST /enrol/lti/tool.php?id=1 HTTP/2.0" 303 753 "<consumer-Moodle url>" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/91.0.4472.77 Safari/537.36"
"GET /course/view.php?id=3 HTTP/2.0" 303 634 "<consumer-Moodle url>" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/91.0.4472.77 Safari/537.36"
"GET /login/index.php HTTP/2.0" 200 22343 "<consumer-Moodle url>" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/91.0.4472.77 Safari/537.36"
while when using the a "Window" option it takes the user to policy acceptance as it should:
"POST /enrol/lti/tool.php?id=1 HTTP/2.0" 303 753 "<consumer-Moodle url>" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/91.0.4472.77 Safari/537.36"
"GET /course/view.php?id=3 HTTP/2.0" 303 573 "<consumer-Moodle url>" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/91.0.4472.77 Safari/537.36"
"GET /admin/tool/policy/index.php HTTP/2.0" 303 840 "<consumer-Moodle url>" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/91.0.4472.77 Safari/537.36"
"GET /admin/tool/policy/view.php?versionid=1&returnurl=https%3A%2F%2F<provider-Moodle url>%2Fadmin%2Ftool%2Fpolicy%2Findex.php&numpolicy=1&totalpolicies=1 HTTP/2.0" 200 71005 "<consumer-Moodle url>" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/91.0.4472.77 Safari/537.36"
EDIT1:
Okay actually this error seems to only occur when using incognito mode to access the consumer moodle and then clicking on the lti item and it works as expected in guest or normal mode, so I guess it is fine.
I assume this is due to the fact that chrome introduced the blocking of third party apps by default some time back (https://support.google.com/chrome/answer/9977812?hl=en) but that is just a guess.