You can use the argument list of group_left to include extra labels from the right operand (parentheses and indents for clarity):

(
  max(consul_health_service_status{status="critical"}) 
  by (service_name,status,node) == 1
)
   + on(service_name,node) group_left(env)
(
   0 * consul_service_tags
)

The important part here is the operation + on(service_name,node) group_left(env):

• the + is "abused" as a join operator (fine since 0 * consul_service_tags always has the value 0)
• group_left(env) is the modifier that includes the extra label env from the right (consul_service_tags)

For now the only solution I have is with query duplication:

(
  (sum(kafka_consumergroup_lag[1d]) by (consumergroup) >= 100)
  * on(consumergroup) group_left(team)
  catalog_entities_info
)
or ignoring(team) (sum(kafka_consumergroup_lag[1d]) by (consumergroup) >= 100)

First half will add team label where possible, and second or half will add missed data (important to merge vectors while ignoring added team label, otherwise we will have duplicates).

I think the keyword in that comment is shareable or in other words reusable rules. Meaning you (often) preserve more labels while using ignoring compared to on and the results will be (usually) a rule with more of it's original labels left intact, so it can be reused for more scenarios.

Imagine these time series:

instance_cpu_time_ns{app="lion", proc="web", rev="34d0f99", env="prod", job="cluster-manager"}
instance_cpu_time_ns{app="elephant", proc="worker", rev="34d0f99", env="prod", job="cluster-manager"}
instance_cpu_time_ns{app="turtle", proc="api", rev="4d3a513", env="prod", job="cluster-manager"}
instance_cpu_time_ns{app="fox", proc="widget", rev="4d3a513", env="prod", job="cluster-manager"}
...

A query with ignoring(rev) leaves out all the other labels in the result, compared with the same query with on(app).

But the result of on and ignoring would be identical if you use them with mutually exclusive set of labels, like the example you are mentioning.

It is possible using unless operator:

item_stock unless item_purchases

Results in a vector consisting of the elements of item_stock for which there are no elements in item_purchases with exactly matching label sets. All matching elements in both vectors are dropped.

Note that the metrics in question do not have 'exactly matching label sets' (name is common but count and in_stock are not). In this case you can use on to set the list of labels to match:

item_stock unless on(name) item_purchases