The service project and the host project both have a private DNS zone named as "ipi-xpn-private-zone". The thing is, although platform.gcp.privateDNSZone.project is set as the host project, the installer checks the zone of the service project, and complains dns name not match. 

$ openshift-install version
openshift-install 4.12.0-0.nightly-2022-10-25-210451
built from commit 14d496fdaec571fa97604a487f5df6a0433c0c68
release image registry.ci.openshift.org/ocp/release@sha256:d6cc07402fee12197ca1a8592b5b781f9f9a84b55883f126d60a3896a36a9b74
release architecture amd64

Always, if both the service project and the host project have a private DNS zone with the same name.

1. try IPI installation to a shared VPC, using "privateDNSZone" of the host project

$ openshift-install create cluster --dir test7
INFO Credentials loaded from file "/home/fedora/.gcp/osServiceAccount.json" 
ERROR failed to fetch Metadata: failed to load asset "Install Config": failed to create install config: platform.gcp.privateManagedZone: Invalid value: "ipi-xpn-private-zone": dns zone jiwei-1026a.qe1.gcp.devcluster.openshift.com. did not match expected jiwei-1027a.qe-shared-vpc.qe.gcp.devcluster.openshift.com 
$ 

The installer should check the private zone in the specified project (i.e. the host project).

$ yq-3.3.0 r test7/install-config.yaml platform
gcp:
  projectID: openshift-qe
  region: us-central1
  computeSubnet: installer-shared-vpc-subnet-2
  controlPlaneSubnet: installer-shared-vpc-subnet-1
  createFirewallRules: Disabled
  publicDNSZone:
    id: qe-shared-vpc
    project: openshift-qe-shared-vpc
  privateDNSZone:
    id: ipi-xpn-private-zone
    project: openshift-qe-shared-vpc
  network: installer-shared-vpc
  networkProjectID: openshift-qe-shared-vpc
$ yq-3.3.0 r test7/install-config.yaml baseDomain
qe-shared-vpc.qe.gcp.devcluster.openshift.com
$ yq-3.3.0 r test7/install-config.yaml metadata
creationTimestamp: null
name: jiwei-1027a
$ 
$ openshift-install create cluster --dir test7
INFO Credentials loaded from file "/home/fedora/.gcp/osServiceAccount.json" 
ERROR failed to fetch Metadata: failed to load asset "Install Config": failed to create install config: platform.gcp.privateManagedZone: Invalid value: "ipi-xpn-private-zone": dns zone jiwei-1026a.qe1.gcp.devcluster.openshift.com. did not match expected jiwei-1027a.qe-shared-vpc.qe.gcp.devcluster.openshift.com 
$ 
$ gcloud --project openshift-qe-shared-vpc dns managed-zones list --filter='name=qe-shared-vpc'
NAME           DNS_NAME                                        DESCRIPTION  VISIBILITY
qe-shared-vpc  qe-shared-vpc.qe.gcp.devcluster.openshift.com.               public
$ gcloud --project openshift-qe-shared-vpc dns managed-zones list --filter='name=ipi-xpn-private-zone'
NAME                  DNS_NAME                                                    DESCRIPTION                         VISIBILITY
ipi-xpn-private-zone  jiwei-1027a.qe-shared-vpc.qe.gcp.devcluster.openshift.com.  Preserved private zone for IPI XPN  private
$ gcloud dns managed-zones list --filter='name=ipi-xpn-private-zone'
NAME                  DNS_NAME                                       DESCRIPTION                         VISIBILITY
ipi-xpn-private-zone  jiwei-1026a.qe1.gcp.devcluster.openshift.com.  Preserved private zone for IPI XPN  private
$ 
$ gcloud --project openshift-qe-shared-vpc dns managed-zones describe qe-shared-vpc
cloudLoggingConfig:
  kind: dns#managedZoneCloudLoggingConfig
creationTime: '2020-04-26T02:50:25.172Z'
description: ''
dnsName: qe-shared-vpc.qe.gcp.devcluster.openshift.com.
id: '7036327024919173373'
kind: dns#managedZone
name: qe-shared-vpc
nameServers:
- ns-cloud-b1.googledomains.com.
- ns-cloud-b2.googledomains.com.
- ns-cloud-b3.googledomains.com.
- ns-cloud-b4.googledomains.com.
visibility: public
$ 
$ gcloud --project openshift-qe-shared-vpc dns managed-zones describe ipi-xpn-private-zone         
cloudLoggingConfig:
  kind: dns#managedZoneCloudLoggingConfig
creationTime: '2022-10-27T08:05:18.332Z'
description: Preserved private zone for IPI XPN
dnsName: jiwei-1027a.qe-shared-vpc.qe.gcp.devcluster.openshift.com.
id: '5506116785330943369'
kind: dns#managedZone
name: ipi-xpn-private-zone
nameServers:
- ns-gcp-private.googledomains.com.
privateVisibilityConfig:
  kind: dns#managedZonePrivateVisibilityConfig
  networks:
  - kind: dns#managedZonePrivateVisibilityConfigNetwork
    networkUrl: https://www.googleapis.com/compute/v1/projects/openshift-qe-shared-vpc/global/networks/installer-shared-vpc
visibility: private
$ 
$ gcloud dns managed-zones describe ipi-xpn-private-zone
cloudLoggingConfig:
  kind: dns#managedZoneCloudLoggingConfig
creationTime: '2022-10-26T06:42:52.268Z'
description: Preserved private zone for IPI XPN
dnsName: jiwei-1026a.qe1.gcp.devcluster.openshift.com.
id: '7663537481778983285'
kind: dns#managedZone
name: ipi-xpn-private-zone
nameServers:
- ns-gcp-private.googledomains.com.
privateVisibilityConfig:
  kind: dns#managedZonePrivateVisibilityConfig
  networks:
  - kind: dns#managedZonePrivateVisibilityConfigNetwork
    networkUrl: https://www.googleapis.com/compute/v1/projects/openshift-qe-shared-vpc/global/networks/installer-shared-vpc
visibility: private
$