How to Find the Page ObjectName and RecordId of an Open Form Page in Creatio?

This is possible, but only from the context of the page itself. I am not sure if it's possible from a sidebar to know anything about the current page loaded elsewhere, maybe with a request handler in a remote module where you can specify the scopes?

As for getting this info within the context of the page, to get the primary data source, you can use: 

const pds = await request.$context.getPrimaryModelName();

With the data source name, you can get the schema for the datasource which will give you the entity/object name, the Id column attribute, and also the primary display value attribute using the following (note, this gets the attribute names, not the values): 

const pds = await request.$context.getPrimaryModelName();
const schema = await request.$context.dataSchemas[pds];
 
const entityName = await schema.name;
const idColumn = await schema.primaryAttributeName;
const nameColumn = await schema.primaryDisplayAttributeName;

Now that you have the attribute names, you can get the values: 

const idValue = await request.$context[idColumn];
const nameValue = await request.$context[nameColumn];
// etc

This sort of thing works great if you have a custom base page type that could be used for many different pages/objects. 

Also, as a FYI, not sure how this is going to change after 8.2.3 since 8.2.3 has a beta feature (not enabled out of the box) that allows a page to have multiple connected data sources. That might break some of this.

Ryan