In OCP, for any CR "xxxxxx.operator cluster":
Updating logLevel field, then the operand pods will renew and their log level will change accordingly.

Updating operatorLogLevel, then the operator pod logs' verbosity will change accordingly.

Take openshift-apiserver operator for example:
For operand, update logLevel:
$ oc patch --type=merge openshiftapiserver.operator cluster -p='{"spec":{"logLevel":"Trace"}}'
openshiftapiserver.operator.openshift.io/cluster patched

Operand pods are renewed:
$ oc get po -n openshift-apiserver
NAME                         READY   STATUS    RESTARTS   AGE
apiserver-7b7c6dc9c4-75xrh   2/2     Running   0          2m11s
apiserver-7b7c6dc9c4-dhj7d   2/2     Running   0          1m44s
apiserver-7b7c6dc9c4-lzwnl   2/2     Running   0          18s

Operand pod log level changes to -v=6, i.e. "Trace":
$ oc get po -n openshift-apiserver apiserver-7b7c6dc9c4-lzwnl -o yaml
...
      exec openshift-apiserver start ... -v=6
...

For operator, update operatorLogLevel:
$ oc patch --type=merge openshiftapiserver.operator cluster -p='{"spec":{"operatorLogLevel":"TraceAll"}}'
openshiftapiserver.operator.openshift.io/cluster patched

$ oc get event -n openshift-apiserver-operator
38s       Normal   OperatorLogLevelChange   namespace/openshift-apiserver-operator   Operator log level changed from "Normal" to "TraceAll"

Operator pod's logs become verbose as per the Response Body's verbosity:
$ oc logs <operator pod> -n openshift-apiserver-operator
...
I0311 12:22:31.498722       1 request.go:1171] Response Body: {"kind":"Event",..."reason":"OperatorLogLevelChange","message":"Operator log level changed from \"Normal\" to \"TraceAll\"","source":{"component":"openshift-apiserver-operator-loggingsyncer"},...}
I0311 12:22:31.500004       1 request.go:1169] Response Body:
00000000  6b 38 73 00 0a 0f 0a 02  76 31 12 09 43 6f 6e 66  |k8s.....v1..Conf|
00000010  69 67 4d 61 70 12 a0 08  0a cd 01 0a 05 61 75 64  |igMap........aud|
...


However, for cert-manager operator, for CR "certmanager.operator":
$ oc get certmanager.operator cluster -o yaml
...
spec:
  logLevel: Normal
  managementState: Managed
  observedConfig: null
  operatorLogLevel: Normal
...

Updating them:
$ oc patch --type=merge certmanager.operator cluster -p='{"spec":{"logLevel":"Trace"}}'

$ oc patch --type=merge certmanager.operator cluster -p='{"spec":{"operatorLogLevel":"TraceALL"}}'

$ oc get certmanager.operator cluster -o yaml
...
spec:
  logLevel: Trace
  managementState: Managed
  observedConfig: null
  operatorLogLevel: TraceALL
...

Then check operand pods:
$ oc get po -n cert-manager
NAME                                       READY   STATUS    RESTARTS   AGE
cert-manager-cainjector-75fcd87cd4-lh5qf   1/1     Running   0          48m
cert-manager-d464b7449-p7ggf               1/1     Running   0          48m
cert-manager-webhook-6c7678c88f-2dz5v      1/1     Running   0          48m

They are not renewed.
Log level is not changed:
$ oc get po -n cert-manager -o yaml | grep '\--v'
      - --v=2
      - --v=2
      - --v=2

Check operator pod, the pod's logs' verbosity is not changed.

cert-manager operator of bundle version v1.10.2-18

Always

1. As above

logLevel and operatorLogLevel fields do not work for "certmanager.operator"

logLevel and operatorLogLevel fields should respectively work for operand and operator, like any other instances of "xxxxxx.operator"s in OCP as above openshiftapiserver.operator example.

Otherwise these fields' presence in "oc get certmanager.operator cluster -o yaml" will confuse users.

Despite users can change operand log level via https://github.com/openshift/cert-manager-operator/pull/95 .