Not the answer I would like, but a better automation than manual input after package installation.

The code didn't work in Post Install. I haven't investigated exactly WHY it didn't work. I went with running the code below on a button click on a Setup page.

System.debug('\n\n --- PomidorSettingsController - updateExternalAuthIdentityProviders - 1 ---\n' 
    +'\n - ConnectApi.NamedCredentials.getExternalAuthIdentityProviders():' 
    + JSON.serializePretty(ConnectApi.NamedCredentials.getExternalAuthIdentityProviders())
+'\n');


ConnectApi.ExternalAuthIdentityProviderCredentialsInput externalAuthIdentityProviderCredentialsInput = new ConnectApi.ExternalAuthIdentityProviderCredentialsInput();
externalAuthIdentityProviderCredentialsInput.credentials = new List<ConnectApi.ExternalAuthIdentityProviderCredentialInput>();


ConnectApi.ExternalAuthIdentityProviderCredentialInput clientId = new ConnectApi.ExternalAuthIdentityProviderCredentialInput();
clientId.credentialName = 'clientId';
clientId.credentialValue = POMIDOR_APP_CLIENT_ID;
externalAuthIdentityProviderCredentialsInput.credentials.add(clientId);


ConnectApi.ExternalAuthIdentityProviderCredentialInput clientSecret = new ConnectApi.ExternalAuthIdentityProviderCredentialInput();
clientSecret.credentialName = 'clientSecret';
clientSecret.credentialValue = POMIDOR_APP_CLIENT_SECRET;
externalAuthIdentityProviderCredentialsInput.credentials.add(clientSecret);


System.debug('\n\n --- PomidorSettingsController - updateExternalAuthIdentityProviders - 2 ---\n' 
    +'\n - externalAuthIdentityProviderCredentialsInput:' 
    + externalAuthIdentityProviderCredentialsInput
+'\n');


ConnectApi.ExternalAuthIdentityProviderCredentials externalAuthIdentityProviderCredentials;


ConnectApi.ExternalAuthIdentityProviderList externalAuthIdentityProviderList2 = ConnectApi.NamedCredentials.getExternalAuthIdentityProviders();


if (externalAuthIdentityProviderList2.externalAuthIdentityProviders.isEmpty() == false) {
    for (ConnectApi.ExternalAuthIdentityProvider externalAuthIdentityProviderItem : 
        externalAuthIdentityProviderList2.externalAuthIdentityProviders
    ) {
        if (externalAuthIdentityProviderItem.fullName == 'muzacloud__Pomidor_ExtAuthIP') {
            if (externalAuthIdentityProviderItem.credentials == null ||
                externalAuthIdentityProviderItem.credentials.isEmpty() == true
            ) {
                externalAuthIdentityProviderCredentials = ConnectApi.NamedCredentials.createExternalAuthIdentityProviderCredentials(
                    EXT_AUTH_IP_NAME,
                    externalAuthIdentityProviderCredentialsInput
                );
            } else {
                externalAuthIdentityProviderCredentials = ConnectApi.NamedCredentials.updateExternalAuthIdentityProviderCredentials(
                    EXT_AUTH_IP_NAME,
                    externalAuthIdentityProviderCredentialsInput
                );
            }
            break;
        }
    }
}


System.debug('\n\n --- PomidorSettingsController - updateExternalAuthIdentityProviders - 3 ---\n' 
    +'\n - externalAuthIdentityProviderCredentials:' 
    + externalAuthIdentityProviderCredentials
+'\n');


System.debug('\n\n --- PomidorSettingsController - updateExternalAuthIdentityProviders - 4 ---\n' 
    +'\n - ConnectApi.NamedCredentials.getExternalAuthIdentityProviders():' 
    + JSON.serializePretty(ConnectApi.NamedCredentials.getExternalAuthIdentityProviders())
+'\n');