Describe the bug

This may be related to #32120, but it's different enough I decided to create a separate issue.
2.166.0 works. 2.167.0 and 2.167.2 do not work.
Credentials File

[role0]
aws_access_key_id        = XXXXX
aws_secret_access_key    = XXXXX
aws_session_token        = XXXXX
aws_security_token       = XXXXX
x_principal_arn          = XXXXX
x_security_token_expires = XXXXX

[role1]
source_profile = role0
role_arn       = arn:aws:iam::12345:role/Role1

[role2]
source_profile = role1
role_arn       = arn:aws:iam::12345:role/Role2

Not sure if it's relevant, but role0 is for Account A and role1 and role2 are for Account B.
Using version 2.167.0, cdk synth --profile role1 works correctly, the CDK_DEFAULT_ACCOUNT environment variable is populated. The issue happens when running cdk synth --profile role2, CDK_DEFAULT_ACCOUNT is not populated. But CDK_DEFAULT_REGION is still populated correctly.

Please let me know if there is any additional information I can provide.

Regression Issue

• Select this option if this issue appears to be a regression.

Last Known Working CDK Version

2.166.0

Expected Behavior

I would expect cdk synth --profile role2 to populate CDK_DEFAULT_ACCOUNT with the account number.

Current Behavior

cdk synth --profile role2 does not populate CDK_DEFAULT_ACCOUNT with the account number.

Reproduction Steps

Run cdk synth on any stack with a profile that is "double assumed".

Possible Solution

No response

Additional Information/Context

No response

CDK CLI Version

2.167.2

Framework Version

No response

Node.js Version

v20.17.0

OS

Windows 10

Language

Python

Language Version

No response

Other information

No response