Gravity Forms comes on a subscription model (we have the Business Legacy License) which provides us with a license key. We use that to activate the plugin in our multi-sites.
#1 Issue – Maximum amount of sites exceeded
We seem to have gone over our allowed sites with our legacy license.
As that license does not support multi-sites environments like ours, and because we have it active on each single one, we are considered to have activated 89 sites (well beyond the allowed 3).

POSSIBLE SOLUTION
The form works nevertheless.
We think that the license key is needed to download the plugin – which is not available within the WordPress environment, but only as a direct download. We then need to upload it as zip file, and then we are asked to enter the license again. But the disclaimer that appears only states that the license needs to be valid to access auto-updates and support.

The form works as expected even with an invalid license key.
We will eventually upgrade to an up-to-date plan in the near future, but for the scope of moving to Kinsta we have decided to leave things as they are.
#2 Issue – Importing the plugin does not import previous entries
We have tested the import/export feature available within the plugin for the Kinsta migration purpose.
Forms are cloned correctly and work as expected within the new Kinsta environment, but previous entries are not there.
Upon researching, we found out that this a premium feature only available via purchasing a paid addon.
In other words, entries can be exported (as a CSV file) via Gravity Forms, but need an addon if we then want to import them into the new site: this involves database mapping and de-serializing, which is not a straightforward process, so it kind of makes sense for it be a premium feature.
SOLUTION
We decided to ask our clients if they need access to existing entries for their day to day needs.
We tend to think that it will not be the case, so we would just download the CSV file and have it available as a backup just in case.
If they do need access within WordPress, we would consider purchasing the addon so we can move them on the new Kinsta sites.