Red Hat Satellite engineering is moving the tracking of its product development work on Satellite to Red Hat Jira (issues.redhat.com). If you're a Red Hat customer, please continue to file support cases via the Red Hat customer portal. If you're not, please head to the "Satellite project" in Red Hat Jira and file new tickets here. Individual Bugzilla bugs will be migrated starting at the end of May. If you cannot log in to RH Jira, please consult article #7032570. That failing, please send an e-mail to the RH Jira admins at rh-issues@redhat.com to troubleshoot your issue as a user management inquiry. The email creates a ServiceNow ticket with Red Hat. Individual Bugzilla bugs that are migrated will be moved to status "CLOSED", resolution "MIGRATED", and set with "MigratedToJIRA" in "Keywords". The link to the successor Jira issue will be found under "Links", have a little "two-footprint" icon next to it, and direct you to the "Satellite project" in Red Hat Jira (issue links are of type "https://issues.redhat.com/browse/SAT-XXXX", where "X" is a digit). This same link will be available in a blue banner at the top of the page informing you that that bug has been migrated.

Verified with Sat 6.13.1 snap 1.0.

Used reproducers from OP. Furthermore, "git grep -l 'H': git grep -l 'Host details' | grep -v -e tests -e locale" shows that there is "Host details" button in one more place: Got to Monitoring -> Audit and search for "type = host", then open some of the found items and the buttong is in the top right corner of the item.
Using all three approaches and clicking the button, I landed on the new host details page.

Since the problem described in this bug report should be
resolved in a recent advisory, it has been closed with a
resolution of ERRATA.

For information on the advisory (Moderate: Satellite 6.13.1 Async Security Update), and where to find the updated
files, follow the link below.

If the solution does not work for you, open a new bug report.

https://access.redhat.com/errata/RHSA-2023:3387