The feature to share a panel by direct link should not be a limitation in Grafana Cloud. I tested this myself just now and saw some odd behavior though. The direct link rendered image URL for my first test dashboard took a whopping 58 seconds to load, while my second test dashboard in another region took about 7 seconds. This delay might be related to an ongoing incident we have, as my first test is in the us-prod-central-0 region while the second test is not. I will continue to investigate this with my team to determine why the response time is so long.
For alternative sharing options, you can choose to use the Snapshot option as you mentioned, using the Grafana UI. I found a related issue regarding the discouraging sentence you found in our docs that clarifies the snapshot API is intended to be used by the Grafana UI only.