So with:
juju model-config -m controller logging-config="<root>=INFO;#charmhub=TRACE"

I was able to get debug-log to spit out what queries it is doing against charmhub.
To start with, it is very poor that `juju info loki-k8s --channel edge/325` is unable to give any responses about the charm.

We start by trying to resolve what loki-k8s in channel 'edge/325' is. (note that we do supply an architecture, as Juju has a default architecture, but shouldn't have a default base):

machine-0: 17:56:47 TRACE juju.apiserver.charms.charmhubrepo.client charmhub Refresh(charmhub.executeOne{
    ID:          "",
    Name:        "loki-k8s",
    Revision:    (*int)(nil),
    Channel:     &"edge/325",
    Base:        charmhub.RefreshBase{Architecture:"amd64", Name:"", Channel:""},
    action:      "install",
    instanceKey: "bf312794-0e9f-4a32-85d7-ed858b3c0425",
    fields:      {"bases", "config-yaml", "download", "id", "license", "metadata-yaml", "name", "publisher", "resources", "revision", "summary", "type", "version"},
})

Unfortunately the response that comes back (which is meant to help us select the base), doesn't actually include the channel that we requested:
{
  "error-list": [],
  "results": [
    {
      "charm": null,
      "error": {
        "code": "revision-not-found",
        "extra": {
          "releases": [
            { "base": { "architecture": "amd64", "channel": "20.04", "name": "ubuntu" }, "channel": "stable" },
            { "base": { "architecture": "amd64", "channel": "20.04", "name": "ubuntu" }, "channel": "candidate" },
            { "base": { "architecture": "amd64", "channel": "20.04", "name": "ubuntu" }, "channel": "beta" },
            { "base": { "architecture": "amd64", "channel": "20.04", "name": "ubuntu" }, "channel": "edge" },
            { "base": { "architecture": "amd64", "channel": "20.04", "name": "ubuntu" }, "channel": "1.0/stable" },
            { "base": { "architecture": "amd64", "channel": "20.04", "name": "ubuntu" }, "channel": "1.0/candidate" },
            { "base": { "architecture": "amd64", "channel": "20.04", "name": "ubuntu" }, "channel": "1.0/beta" },
            { "base": { "architecture": "amd64", "channel": "20.04", "name": "ubuntu" }, "channel": "1.0/edge" }
          ]
        },
        "message": "No revision was found in the Store."
      },
      "id": "VpRGTlLZZh1ON756aodclPgvrXBZHrCN",
      "instance-key": "bf312794-0e9f-4a32-85d7-ed858b3c0425",
      "name": "loki-k8s",
      "released-at": null,
      "result": "error"
    }
  ]
}


At a minimum, we should understand the error response a little bit better. It isn't that there is an ambiguous architecture (one is supplied, and only that is returned), it is that the channel only returns 20.04 as available, but none of the channels that are returned are the one that was requested. 

I get the same error if I specify "--channel latest/edge/325".

Now, to start with, the fact that we asked charmhub "I need to know what `loki-k8s` channel=`edge/325`" means, and it doesn't come back with a response that includes the channel that we asked for is certainly a problem.

If you do specify a base, so that the automatic lookup doesn't need to happen, then it appears to work:
$ juju deploy loki-k8s --channel latest/edge/325 --base ubuntu@20.04

As you noted, requesting 'ubuntu@22.04' doesn't work (or series=jammy) because there isn't a charm there.