I have a Solis inverter, although I don't use the cloud / this integration myself.
HA integrations such as this are mostly written by enthusiasts, and you can often find the development source on GitHub, where there may well be additional documentation as well as sections for help, issues and discussions.
In this case, the GitHub repository is at https://github.com/mkuthan/solis-cloud-control
where there is good documentation.
On your first point - there is a given list of supported inverters. The S5-GR3P5K is on this list, so yes this is recognised. Your other inverter is not on the list, and either cannot be added or you will have to reach out to the integration author to ask about your specific model. There is a note at the bottom of the supported inverter list on how to do this.
On your second point - the integration does nothing more than provide access to the Solis cloud-based controls that you can probably see using the standard Solis cloud app. These will expose, to the cloud, the specific controls available for the inverter, which clearly depend on the particular model. My hybrid inverter has many controls for SOC setting, for energy storage modes, and timed charge / discharge. I have looked for the manual for the S5-GR3(5)K, and this suggests that the inverter settings include only the date/time and inverter id address. If this is indeed the case, that this inverter model only has settings for date/time, then yes you are likely to only have three entities created by the integration - one for turning the inverter on/off, one for setting the date/time, and perhaps one for setting the id address.
As your inverters are probably not controllable, you may find it more useful to just bring in the various inverter values (power / energy / status). There appears to be a companion integration for cloud-based Solis sensors:
https://github.com/hultenvp/solis-sensor/
That integration should work for you and will provide a great deal more useful information.
