Assigning custom Lightning Record Pages to standard Lightning console applications

This is working as designed.

In standard Salesforce console applications, some objects have a system app default record page. For those objects, if you assign a custom Lightning Record Page as the org default, it doesn't display to users.

Note: To perform the following steps, make sure you have the Permission to "Manage Profiles and Permission Sets".

 To see what Lightning Record Page is currently assigned to an application use the following steps:

1. In Lightning Experience, click Setup | Object Manager
2. Select an Object from the list
3. Select Lightning Record Pages from the left-hand panel
4. Click on the View Page Assignments button in the top right corner
5. In the Look Up an Assignment box, select a value for each of the the available App, Record Type, and Profile picklists
6. Select the Find Page button
7. Review the Page Displayed section that appears
8. If the Page Displayed shows App System Default, this indicates that the console application is using the system app default record page and not a custom Lightning Record Page.

To assign a custom Lightning Record Page to a standard Salesforce Lightning console application for those objects, assign the custom page as the app default for the standard console applications as follows:

1. Open Lightning Pages after going to Setup >> Object Manager >>Object (eg. Account)
2. Edit the Page you want to use
3. Select Activation action on top right corner
4. Select the App Default tab and then select Assign as App Default

5. In the resulting window, select the app you would like to assign the page as the default page (e.g. Lightning Sales Console)

Note: If the app is not showing in your list, that means it's not a Lightning app and you can't use it for this type of settings. Check App type in App Manager and you'll see if it's the Lightning type or not.